Description
Return one Fibonacci-style boundary-extension sum.
Exact combinatorial recurrences distinguish individual summands, adjacent ratios and complete totals. A local arithmetic identity can be correct without proving that its supplied inputs are the intended counts or that a whole enumeration has been completed.
Return one Fibonacci-style boundary-extension sum.
When to use this tool
Use Fibonacci Tiling Boundary Extension when checking the stated recurrence, coefficient-ratio or inclusion-exclusion term.
How to use the tool and how it works
- Enter previous, beforePrevious. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read count. Use the output convention below.
Return one Fibonacci-style boundary-extension sum. Require nonnegative whole previous/beforePrevious; count = previous+beforePrevious.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| previous | Previous | Required. Safe integer; minimum 0. |
| beforePrevious | Before Previous | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| count | Count | Required. Safe integer. |
{
"input": {
"previous": 5,
"beforePrevious": 3
},
"output": {
"count": 8
}
}Limitations and assumptions
- Inputs and initial conditions are supplied; this does not establish a particular tiling length or a complete enumeration.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete recurrence with justified initial conditions and exact integer arithmetic when a full counting result is required.
References
Similar or alternative tools
- Derangement Recurrence Single Branch
Return one derangement-recurrence branch contribution.
- Catalan Convolution Single Summand
Return one exact Catalan-convolution summand.