A143787 Number of compositions of n into floor((3*j)/2) kinds of j's for all j>=1.

1, 1, 4, 11, 33, 95, 278, 808, 2355, 6856, 19969, 58151, 169353, 493190, 1436288, 4182793, 12181260, 35474611, 103310209, 300862991, 876181998, 2551642760, 7430968523, 21640683328, 63022629465, 183536340391, 534499885849, 1556586163406, 4533135643968, 13201529892305, 38445880553108, 111963215139163, 326062542045345

Offset: 0

Author

Joerg Arndt, Jul 06 2011

Keywords

• nonn

Comments

The g.f. for compositions of k_1 kinds of 1's, k_2 kinds of 2's, ..., k_j kinds of j's, ... is 1/(1-sum(j>=1, k_j * x^j )).

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,3,-1).

Crossrefs

Cf. A121907 (floor((3*j-1)/2)), A055841 (3*j-1), A052156 (2*j-1), A006053 (floor(j/2)), A176848 (floor(j/3)).

Programs

Mathematica

LinearRecurrence[{2,3,-1},{1,1,4,11},50] (* Paolo Xausa, Nov 14 2023 *)

Formula

a(n) = +2*a(n-1) +3*a(n-2) -1*a(n-3).

G.f.: ((1-x)^2*(1+x))/(1-2*x-3*x^2+x^3).

G.f.: 1/(1-sum(j>=1, floor((3*j)/2)*x^j )).