bibkey: oeis2008a152661
authors: Emeric Deutsch; R. J. Mathar
year: 2008
title: "OEIS A152661: permutations whose first two elements have the same parity"
doi: null
url: https://oeis.org/A152661
claim: "The source defines the permutation count for n >= 2 and records Mathar's conjectural first recurrence and prior even/odd formulas."
strata_touched:
  - D5/S3/Combinatorics/Permutation/MatharSameParityRecurrence
license: citation-only
triage: anchor

OEIS A152661

Revision 23 defines a(n), for n >= 2, as the number of permutations of {1,…,n} whose first two elements have the same parity. Its first FORMULA attributes to R. J. Mathar the conjectural recurrence (3-n)a(n) + 2(n-2)a(n-1) + (n-1)(n-2)(n-3)a(n-2) = 0. The same entry gives prior even and odd factorial-binomial formulas.

The Lean definition uses one-based natural labels of permutations of Fin n, casts the subtype cardinality to the integers, and assigns zero for n < 2. This last convention is a repository totalization outside the source domain. The disjoint-fiber count bridge and all-index recurrence proof are repository derivations of the published problem, rather than claims of new counting formulas. No adjacent A077613 identity is asserted.

Verified locator

• URL: https://oeis.org/A152661, revision 23.
• Text: https://oeis.org/search?q=id%3AA152661&fmt=text
• Revision history: https://oeis.org/history?seq=A152661