A366107 a(n) = Sum_{i=0..floor(q(n)/3)} binomial(n-3*(i+1), q(n)-3*i) with q(n) = ceiling((n-3)/2).

1, 1, 2, 3, 6, 11, 21, 39, 75, 141, 273, 519, 1009, 1933, 3770, 7263, 14202, 27479, 53846, 104543, 205216, 399543, 785460, 1532779, 3017106, 5899167, 11624580, 22766607, 44905518, 88073091, 173863965, 341425551, 674506059, 1326019653, 2621371005, 5158412943, 10203609597

Offset: 3

Author

Stefano Spezia, Sep 29 2023

Keywords

• nonn

Links

• 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 (3.5) at p. 4 and (4.15) at p. 8.

Crossrefs

Cf. A004526, A218708, A366108, A366109.

Programs

Mathematica

q[n_]:=Ceiling[(n-3)/2]; a[n_]:=Sum[Binomial[n-3(i+1),q[n]-3i], {i,0,Floor[q[n]/3]}]; Array[a,37,3]

PARI

a(n) = my(q=ceil((n-3)/2)); sum(i=0, q\3, binomial(n-3*(i+1), q-3*i)); \\ Michel Marcus, Sep 30 2023

Formula

From Remark 3.4 at p. 5 in Czédli: (Start)

A366108(n)/a(n) ~ 7/4.

A366109(n)/a(n) ~ 7/6. (End)

a(n) ~ c*2^(n+1)/sqrt(n), with c = 1/(7*sqrt(2*Pi)) = (2/7)* A218708.