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A053798 Number of basis partitions of n+16 with Durfee square size 4.

%I A053798 #21 Jul 02 2025 16:01:59
%S A053798 1,2,4,8,14,22,34,50,70,96,128,166,212,266,328,400,482,574,678,794,
%T A053798 922,1064,1220,1390,1576,1778,1996,2232,2486,2758,3050,3362,3694,4048,
%U A053798 4424,4822,5244,5690,6160,6656,7178,7726,8302,8906,9538,10200,10892,11614
%N A053798 Number of basis partitions of n+16 with Durfee square size 4.
%H A053798 Seiichi Manyama, <a href="/A053798/b053798.txt">Table of n, a(n) for n = 0..10000</a>
%H A053798 M. D. Hirschhorn, <a href="https://doi.org/10.1016/S0012-365X(99)00030-8">Basis partitions and Rogers-Ramanujan partitions</a>, Discrete Math. 205 (1999), 241-243.
%H A053798 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,3,-1)
%F A053798 G.f.: (1+q)(1+q^2)(1+q^3)(1+q^4)/((1-q)(1-q^2)(1-q^3)(1-q^4)).
%F A053798 a(n) = (n*(n^2+15)+2*A049347(n-1))/9, n>0. G.f. 1+ 2*x*(1-x+x^2-x^3+x^4) / ( (1+x+x^2)*(x-1)^4 ). - _R. J. Mathar_, Mar 24 2011
%t A053798 LinearRecurrence[{3,-3,2,-3,3,-1},{1,2,4,8,14,22,34},50] (* _Harvey P. Dale_, Dec 29 2019 *)
%K A053798 easy,nonn
%O A053798 0,2
%A A053798 _James Sellers_, Mar 27 2000