A366109 - OEIS

A366109

a(n) = floor(n!*(3*floor(n/2)!*ceiling(n/2)! + 3*floor((n+2)/2)!*ceiling((n-2)/2)! - 6*floor(n/2)!*ceiling((n-2)/2)!)^(-1)).

1, 1, 2, 4, 7, 13, 26, 46, 92, 168, 333, 616, 1225, 2288, 4558, 8580, 17107, 32413, 64664, 123170, 245832, 470288, 938943, 1802770, 3600207, 6933733, 13849778, 26744400, 53429368, 103411680, 206621384, 400720260, 800747232, 1555737480, 3109074130, 6050090200, 12091800773

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OFFSET

3,3

LINKS

Table of n, a(n) for n=3..39.

Gábor Czédli, Minimum-sized generating sets of the direct powers of the free distributive lattice on three generators and a Sperner theorem, arXiv:2309.13783 [math.CO], 2023. See formulas (3.6) at p. 4 and (4.15) at p. 8.

FORMULA

a(n)/A366107(n) ~ 7/6 (see Remark 3.4 at p. 5 in Czédli).

a(n) ~ c*2^n/sqrt(n), with c = 1/(3*sqrt(2*Pi)) = (2/3)*A218708.

MATHEMATICA

a[n_]:=Floor[n!(3Floor[n/2]!Ceiling[n/2]! + 3Floor[(n+2)/2]!Ceiling[(n-2)/2]! - 6Floor[n/2]!Ceiling[(n-2)/2]!)^(-1)]; Array[a, 37, 3]

CROSSREFS