bibkey: kimberling2022a077866 authors: Clark Kimberling year: 2022 title: “OEIS A077866: Expansion of (1-x)^(-1)/(1-x-2x^2+2x^3)” doi: null url: https://oeis.org/A077866 claim: “Conjecture: let b(n) be the number of subsets S of {1,2,…,n} having more than one element such that (sum of least two elements of S) = max(S). Then b(0) = b(1) = b(2) = 0 and b(n+3) = a(n) for n >= 0.” strata_touched:

• D5/S3/Combinatorics/KimberlingLeastTwoSubsetCount license: citation-only triage: anchor

OEIS A077866

Kimberling’s comment dated 27 September 2022 states the subset-count conjecture quoted above. The official OEIS text interface returned revision 47 (30 June 2026) on 30 September 2026. The entry defines a(n) by 1/((1-x)*(1-x-2*x^2+2*x^3)); its even and odd formulas are a(2m)=3*2^(m+1)-2*(m+1)-3 and a(2m+1)=2^(m+3)-2*(m+3). The formal sequence uses the equivalent initial values 1,2,5,8 and recurrence a(n+4)+4*a(n+1)=2*a(n+3)+a(n+2)+2*a(n).

The OEIS entry still labels the subset assertion a conjecture in the source check recorded in issue #11414. This note records the wording and sequence identification; it does not claim publication priority.

Verified locator

• URL: https://oeis.org/A077866 (official OEIS text interface, revision 47, retrieved 2026-09-30; %C contains Kimberling’s dated conjecture and %F contains the recurrence and parity formulas).