Sequence Tools
Browse all available sequence tools.
Available tools
- Affine Recurrence Two Step Constant Tool Compose x↦a*x+b with itself and return its affine coefficients.
- Alternating Prefix Balance Tool Calculate alternating prefix balance from explicit caller-supplied inputs.
- Alternating Sequence Sign At Index Shift an explicit alternating sequence sign by the exact parity of a signed index difference.
- Alternating Series Next Term Bound Tool Enclose a convergent alternating series assuming subsequent term magnitudes decrease to zero.
- Arithmetic Geometric Single Term Formula Tool Calculate arithmetic geometric single term formula from explicit caller-supplied inputs.
- Arithmetic Progression Modular Residue Step Tool Calculate arithmetic progression modular residue step from explicit caller-supplied inputs.
- Arithmetic Progression Modulus Residue Tool Compute arithmetic progression modulus residue from explicit bounded inputs.
- Arithmetic Progression One Term Deletion Gap Tool Calculate arithmetic progression one term deletion gap from explicit caller-supplied inputs.
- Arithmetic Sequence Calculator Calculate an arithmetic sequence term and finite sum.
- Arithmetic Sequence Reference Index Shift Shift an explicit arithmetic-sequence reference term by a signed exact integer index displacement.
- Arithmetic Step Direction Flag Tool Calculate arithmetic step direction flag from explicit caller-supplied inputs.
- Bounded Recurrence Zero Input Step Tool Calculate bounded recurrence zero input step from explicit caller-supplied inputs.
- Cumulative Sum Reset Boundary Delta Tool Calculate cumulative sum reset boundary delta from explicit caller-supplied inputs.
- Factorial Ratio Adjacent Logterm Tool Calculate factorial ratio adjacent logterm from explicit caller-supplied inputs.
- Factorial Sequence Ratio At Index Tool Compute factorial sequence ratio at index from explicit bounded inputs.
- Figurate Sequence Inverse Index Discriminant Tool Calculate figurate sequence inverse index discriminant from explicit caller-supplied inputs.
- Finite Difference Binomial Weight Term Tool Calculate finite difference binomial weight term from explicit caller-supplied inputs.
- Finite Difference Leading Sign Tool Report the sign of a degree-order polynomial forward difference on a positive unit grid from its supplied leading coefficient.
- Finite Difference Row Entry Tool Return one entry of the first forward-difference row from adjacent sequence values.
- Finite Sequence Endpoint Parity Compare explicit inclusive integer sequence endpoint parity and count terms with exact index arithmetic.
- Geometric Partial Sum Tail Ratio Tool Calculate geometric partial sum tail ratio from explicit caller-supplied inputs.
- Geometric Progression One Term Insertion Test Tool Calculate geometric progression one term insertion test from explicit caller-supplied inputs.
- Geometric Recurrence Sign Alternation Flag Tool Calculate geometric recurrence sign alternation flag from explicit caller-supplied inputs.
- Geometric Sequence Calculator Calculate a geometric sequence term and finite sum.
- Geometric Sequence Reference Index Shift Shift an explicit geometric-sequence reference term by a signed integer index displacement, requiring a nonzero ratio for backward shifts.
- Geometric Series Single Tail Bound Tool Compute geometric series single tail bound from explicit bounded inputs.
- Harmonic Progression Reciprocal Step Tool Calculate harmonic progression reciprocal step from explicit caller-supplied inputs.
- Interleaved Sequence Odd Even Length Tool Compute interleaved sequence odd even length from explicit bounded inputs.
- Linear Recurrence Coefficient Impulse Term Tool Compute linear recurrence coefficient impulse term from explicit bounded inputs.
- Lucas Recurrence One State Update Tool Calculate lucas recurrence one state update from explicit caller-supplied inputs.
- Period Prefix Remainder Tool Calculate period prefix remainder from explicit caller-supplied inputs.
- Periodic Cycle Missing Slot Budget Tool Calculate periodic cycle missing slot budget from explicit caller-supplied inputs.
- Periodic Interleaving Phase Source Index Tool Calculate periodic interleaving phase source index from explicit caller-supplied inputs.
- Periodic Sample Phase Boundary Token Tool Calculate periodic sample phase boundary token from explicit caller-supplied inputs.
- Polygonal Number Adjacent Gap Tool Calculate polygonal number adjacent gap from explicit caller-supplied inputs.
- Rational Generating Function Coefficient Step Tool One formal power-series coefficient from Q(z)A(z)=P(z), with supplied prior coefficients aligned to Q tail coefficients.
- Recurrence Affine Fixed Point Shift Tool Calculate recurrence affine fixed point shift from explicit caller-supplied inputs.
- Recurrence Coefficient Leading Gap Tool Inspect a supplied leading-to-trailing recurrence coefficient list without solving the recurrence.
- Recurrence Coefficient Unit Consistency Tag Preserve an explicit recurrence term and coefficient unit convention without performing dimensional inference.
- Recurrence Coefficient Zero Leading Flag Flag whether an explicit leading linear-recurrence coefficient permits division without claiming the recurrence is otherwise well posed.
- Recurrence Companion State Index Map Tool Calculate recurrence companion state index map from explicit caller-supplied inputs.
- Recurrence Delay State Shift Index Tool Calculate recurrence delay state shift index from explicit caller-supplied inputs.
- Recurrence Initial State Shift Step Tool Compute recurrence initial state shift step from explicit bounded inputs.
- Recurrence Step Boundary Label Tool Classify an index relative to a recurrence's initial-condition block; the first computed term is initialIndex + order.
- Recurrence Term Modulus Step Evaluate one explicit affine integer recurrence step modulo a supplied positive modulus with exact multiplication.
- Run Boundary Alternation Parity Tool Count alternations in an explicitly supplied two-label run-length encoding, preserving empty-stream status.
- Second Difference One Quadratic Term Tool Calculate second difference one quadratic term from explicit caller-supplied inputs.
- Second Difference Sign Tool Classify one three-term second difference under an explicit tolerance policy, reusing the finite-difference weight primitive with centered observations.
- Second Order Recurrence Characteristic Product Tool For a_n = firstCoefficient*a_(n-1)+secondCoefficient*a_(n-2), return characteristic-root sum and product.
- Second Order Recurrence State Determinant Tool Compute second order recurrence state determinant from explicit bounded inputs.
- Sequence Delay Zero Padding Count Tool Calculate sequence delay zero padding count from explicit caller-supplied inputs.
- Sequence Index Centered Window Parity Tool Compute sequence index centered window parity from explicit bounded inputs.
- Sequence One Step Cumulative Product Ratio Tool Calculate sequence one step cumulative product ratio from explicit caller-supplied inputs.
- Sequence Padded Origin Shift Tool Map an index after left padding to its signed original position, preserving negative padding positions.
- Sequence Run Length Decoded Position Tool Compute sequence run length decoded position from explicit bounded inputs.
- Sequence Symmetric Index Pair Map Tool Calculate sequence symmetric index pair map from explicit caller-supplied inputs.
- Sequence Term Prediction Residual Subtract an explicit predicted sequence term from an observed term on the same quantity basis.
- Sequence Two Run Boundary Count Count resulting runs when two explicit constant-value runs are concatenated, accounting for empty runs and equality.
- Sequence: Arithmetic Term Adjacent Residual Tool Check one adjacent arithmetic recurrence transition against an explicit difference, exposing residual rather than fitting a sequence.
- Sequence: Fibonacci Pair Step Update Tool Advance one exact caller-established Fibonacci-style adjacent integer pair by the recurrence (a,b)->(b,a+b); does not certify the supplied pair belongs to canonical Fibonacci numbers.
- Sequence: Geometric Term Adjacent Residual Tool Check one adjacent geometric recurrence transition against an explicit multiplier, with no division by zero or sequence fitting.
- Sequence: Linear Recurrence First Difference Step Tool Advance one short real linear recurrence with oldest-to-newest state and matching coefficient order, returning next state and its first difference; no symbolic recurrence solving.
- Sequence: Lucas Pair Parity Label Tool Report adjacent canonical Lucas-number parities using L0=2,L1=1 and the period-three parity recurrence; no value enumeration.
- Sequence: Periodic Index Quotient Remainder Tool Decompose a signed sequence index into floor quotient and nonnegative within-period phase, retaining negative cycle numbers.
- Sequence: Sequence Interleave Source Index Tool Resolve one position in an equal-length round-robin interleave to its ordered source and local element index, without constructing the interleave.
- Triangular Number Calculator Calculate the nth triangular number.
- Triangular Sequence Successive Gap Tool Compute triangular sequence successive gap from explicit bounded inputs.