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%I #17 Nov 14 2023 03:28:48
%S 1,1,4,11,33,95,278,808,2355,6856,19969,58151,169353,493190,1436288,
%T 4182793,12181260,35474611,103310209,300862991,876181998,2551642760,
%U 7430968523,21640683328,63022629465,183536340391,534499885849,1556586163406,4533135643968,13201529892305,38445880553108,111963215139163,326062542045345
%N Number of compositions of n into floor((3*j)/2) kinds of j's for all j>=1.
%C 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 )).
%H Paolo Xausa, <a href="/A143787/b143787.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 3, -1).
%F a(n) = +2*a(n-1) +3*a(n-2) -1*a(n-3).
%F G.f.: ((1-x)^2*(1+x))/(1-2*x-3*x^2+x^3).
%F G.f.: 1/(1-sum(j>=1, floor((3*j)/2)*x^j )).
%t LinearRecurrence[{2,3,-1},{1,1,4,11},50] (* _Paolo Xausa_, Nov 14 2023 *)
%Y Cf. A121907 (floor(3*j-1)/2)), A055841 (3*j-1), A052156 (2*j-1), A006053 (floor(j/2)), A176848 (floor(j/3)).
%K nonn
%O 0,3
%A _Joerg Arndt_, Jul 06 2011
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