bibkey: kagey2019a329479
authors: Peter Kagey
year: 2019
title: "OEIS A329479: Binary null polynomials modulo three"
doi: null
url: https://oeis.org/A329479/internal
claim: "Conjectured recurrence: a(n) = 2a(n-1) + 2a(n-2) - 5a(n-3) - 2a(n-4) + 10a(n-5) - 4a(n-6) - 4a(n-7) + 8a(n-8)."
strata_touched:
  - D5/S3/Combinatorics/BinaryNullPolynomials/KageyA329479Recurrence
license: citation-only
triage: anchor

OEIS A329479

Verified locator

Source: https://oeis.org/A329479/internal

Revision 25, NAME and final FORMULA line (unpaginated). Revision discussion: https://oeis.org/history?seq=A329479. There is no identified DOI or arXiv source.

Source statement

Number of degree n polynomials f with all nonzero coefficients equal to 1 such that f(k) is divisible by 3 for all integers k.

Conjectured recurrence: a(n) = 2a(n-1) + 2a(n-2) - 5a(n-3) - 2a(n-4) + 10a(n-5) - 4a(n-6) - 4a(n-7) + 8a(n-8).

The NAME and the six degree-seven examples specify degree exactly n; the coefficient word therefore has n plus one entries. The COMMENT’s string-length wording differs by one. The source offset is one, so the displayed recurrence is interpreted for n at least nine. Its subtraction is integer subtraction. The count is of integer polynomials, not polynomial functions on a residue field.

The source states the recurrence as a conjecture. The repository proof uses a coefficient-word bijection, simultaneous evaluation at one and minus one in ZMod 3, and a finite transfer-column identity. No source theorem relying on the conjectured recurrence was identified in the entry. Completeness of the external literature screen is ASSUMED-UNVERIFIED; its retrieved scope is specified in issue https://github.com/the-omega-institute/trureturing/issues/21714.