Description
Parse current, previous, p, and q as bounded exact decimal integers and return next=p*current-q*previous as decimal text.
A sequence rule specifies an index origin, state order, and relation among terms. Advancing one step, mapping an index, and checking a local residual answer different questions. Supplied coefficients or periods define a model; they do not establish that observations follow it.
Parse current, previous, p, and q as bounded exact decimal integers and return next=p*current-q*previous as decimal text.
When to use this tool
Use Lucas Recurrence One State Update when you need this particular index map, recurrence step, count, or local algebraic term under supplied sequence conventions.
How to use the tool and how it works
- Enter current, previous, p, q. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read next. Use the output convention below.
Parse current, previous, p, and q as bounded exact decimal integers and return next=p*current-q*previous as decimal text.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| current | Current | Required. Text; maximum UTF-16 length 8192. |
| previous | Previous | Required. Text; maximum UTF-16 length 8192. |
| p | Exact decimal first multiplier. | Required. Text; maximum UTF-16 length 8192. |
| q | Exact decimal multiplier subtracted against previous. | Required. Text; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| next | Next | Required. Text; maximum UTF-16 length 8192. |
{
"input": {
"current": "3",
"previous": "1",
"p": "2",
"q": "-1"
},
"output": {
"next": "7"
}
}Limitations and assumptions
- All parameters and the state pair are supplied. This advances the stated generalized Lucas recurrence without proving canonical-sequence membership or applying a plus-q convention.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Choose exact integer arithmetic when the index or coefficient range requires it. A complete sequence analysis needs actual terms and a consistent index and state-order convention beyond one local step.
References
Similar or alternative tools
- Recurrence Companion State Index Map
Return shiftEntry one only for row>0 and column=row-1, and coefficientRow for row zero.
- Recurrence Delay State Shift Index
Return nextIndex=index+1 for a bounded state index except the final position, which returns minus one and dropped true.