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%I #20 Dec 29 2019 17:36:48
%S 1,2,4,8,14,22,34,50,70,96,128,166,212,266,328,400,482,574,678,794,
%T 922,1064,1220,1390,1576,1778,1996,2232,2486,2758,3050,3362,3694,4048,
%U 4424,4822,5244,5690,6160,6656,7178,7726,8302,8906,9538,10200,10892,11614
%N Number of basis partitions of n+16 with Durfee square size 4.
%H Seiichi Manyama, <a href="/A053798/b053798.txt">Table of n, a(n) for n = 0..10000</a>
%H 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 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,3,-1)
%F 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 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 LinearRecurrence[{3,-3,2,-3,3,-1},{1,2,4,8,14,22,34},50] (* _Harvey P. Dale_, Dec 29 2019 *)
%K easy,nonn
%O 0,2
%A _James A. Sellers_, Mar 27 2000
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