Question 7114: Ordered Recurrence Window and Adjacent Differences

Original question and givens

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=1, a_(n+1)=a_n+(0), start=11, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

• G001 — N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. a_0=1, a_(n+1)=a_n+(0), start=11, length=3. Give (window indices, term values, adjacent differences); length=0 gives three empty lists.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-sequence

Step-by-step derivation

N starts at0;ordered finite indices and repeated values retained

given recurrences differ from guessing an infinite rule from observations

a(0)=1;a(n+1)=a(n)+(0)

a(n)=1+n·(0) by this supplied affine recurrence

window start increment := mul(11, 0)

window start increment = 0

window start value := sum(1, 0)

window start value = 1

window recurrence term1 := sum(1, 0)

window recurrence term1 = 1

window recurrence term2 := sum(1, 0)

window recurrence term2 = 1

window adjacent difference0 := sub(1, 1)

window adjacent difference0 = 0

window adjacent difference1 := sub(1, 1)

window adjacent difference1 = 0

window indices=[11, 12, 13];values=[1, 1, 1]

adjacent deltas=[0, 0]

Reverse checks

• S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S008 · premise_and_result_audit — Recompute window adjacent difference1 with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Recompute window adjacent difference0 with exact rational arithmetic, not rounded decimals.
• S006 · premise_and_result_audit — Recompute window recurrence term2 with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Recompute window recurrence term1 with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute window start value with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute window start increment with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

([11, 12, 13], [1, 1, 1], [0, 0])

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.