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A288165 Expansion of x^4/((1-x^4)*(1-x^3)*(1-x^6)*(1-x^9)).

%I A288165 #20 Jan 07 2018 23:59:49
%S A288165 0,0,0,0,1,0,0,1,1,0,2,1,1,3,2,1,5,3,2,6,5,3,9,6,5,11,9,6,15,11,9,18,
%T A288165 15,11,23,18,15,27,23,18,34,27,23,39,34,27,47,39,34,54,47,39,64,54,47,
%U A288165 72,64,54,84,72,64,94,84,72,108,94,84,120,108,94,136,120
%N A288165 Expansion of x^4/((1-x^4)*(1-x^3)*(1-x^6)*(1-x^9)).
%H A288165 Seiichi Manyama, <a href="/A288165/b288165.txt">Table of n, a(n) for n = 0..10000</a>
%H A288165 Daniel Panario, Murat Sahin and Qiang Wang, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i4p55/pdf">Generalized Alcuin’s Sequence</a>, The Electronic Journal of Combinatorics, Volume 19, Issue 4 (2012).
%H A288165 <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 1, 1, 0, 1, -1, 0, 0, -1, 0, -1, 0, 0, -1, 1, 0, 1, 1, 0, 0, -1).
%F A288165 a(n) = p_4(n/3)     if n == 0 mod 3,
%F A288165 a(n) = p_4((n+8)/3) if n == 1 mod 3,
%F A288165 a(n) = p_4((n+4)/3) if n == 2 mod 3,
%F A288165 where p_4(n) is the number of partitions of n into exactly 4 parts.
%e A288165 a(57) = p_4(57/3)     = p_4(19) = A001400(15) = 54,
%e A288165 a(58) = p_4((58+8)/3) = p_4(22) = A001400(18) = 84,
%e A288165 a(59) = p_4((59+4)/3) = p_4(21) = A001400(17) = 72,
%e A288165 a(60) = p_4(60/3)     = p_4(20) = A001400(16) = 64,
%e A288165 a(61) = p_4((61+8)/3) = p_4(23) = A001400(19) = 94,
%e A288165 a(62) = p_4((62+4)/3) = p_4(22) = A001400(18) = 84.
%Y A288165 Cf. A001400, A029253.
%Y A288165 Cf. A005044 (k=3), this sequence (k=4), A288166 (k=5).
%K A288165 nonn,easy
%O A288165 0,11
%A A288165 _Seiichi Manyama_, Jun 06 2017