A366108 -id:A366108 - cp's OEIS frontend

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

Stefano Spezia, Sep 29 2023

nonn

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.

Cf. A004526, A218708, A366108, A366109.

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]

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

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.

A366109 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)).

Original entry on oeis.org

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

Offset: 3

Stefano Spezia, Sep 29 2023

nonn

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.

Cf. A000142, A004526, A081123, A218708, A366107, A366108.

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]

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.

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A366109 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)).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

cp's OEIS Frontend

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).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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)).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

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

A366109 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)).