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 A143787 Number of compositions of n into floor((3*j)/2) kinds of j's for all j>=1. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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). 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 )). MATHEMATICA LinearRecurrence[{2, 3, -1}, {1, 1, 4, 11}, 50] (* Paolo Xausa, Nov 14 2023 *) CROSSREFS Cf. A121907 (floor(3*j-1)/2)), A055841 (3*j-1), A052156 (2*j-1), A006053 (floor(j/2)), A176848 (floor(j/3)). Sequence in context: A034745 A217860 A307073 * A289973 A236583 A282990 Adjacent sequences: A143784 A143785 A143786 * A143788 A143789 A143790 KEYWORD nonn AUTHOR Joerg Arndt, Jul 06 2011 STATUS approved

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Last modified July 20 18:59 EDT 2024. Contains 374459 sequences. (Running on oeis4.)