Description
Return start=center-floor((width-1)/2), endExclusive=start+width, and centeredExactly for odd width.
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.
Return start=center-floor((width-1)/2), endExclusive=start+width, and centeredExactly for odd width.
When to use this tool
Use Sequence Index Centered Window Parity 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 center, width. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read start, endExclusive, centeredExactly. Inspect centeredExactly before interpreting the associated values.
Return start=center-floor((width-1)/2), endExclusive=start+width, and centeredExactly for odd width. Require nonnegative integer center, positive integer width, and nonnegative resulting start.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| center | Center | Required. Safe integer; minimum 0. |
| width | Width | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| start | Start | Required. Safe integer. |
| endExclusive | End Exclusive | Required. Safe integer. |
| centeredExactly | Whether width is odd under the selected index placement. | Required. Boolean. |
{
"input": {
"center": 5,
"width": 3
},
"output": {
"start": 4,
"endExclusive": 7,
"centeredExactly": true
}
}Limitations and assumptions
- Even widths place the extra position on the upper-index side. No data length or end bound is supplied, so the window can extend beyond an actual sequence.
- 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
- Sequence: Lucas Pair Parity Label
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
Decompose a signed sequence index into floor quotient and nonnegative within-period phase, retaining negative cycle numbers.