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A053800 Number of basis partitions of n+25 with Durfee square size 5.

%I A053800 #17 Jul 02 2025 16:01:59
%S A053800 1,2,4,8,14,24,38,58,86,124,174,238,320,422,548,702,886,1106,1366,
%T A053800 1670,2024,2432,2900,3434,4040,4724,5492,6352,7310,8374,9552,10850,
%U A053800 12278,13844,15556,17424,19456,21662,24052,26636,29424,32426,35654,39118
%N A053800 Number of basis partitions of n+25 with Durfee square size 5.
%H A053800 Seiichi Manyama, <a href="/A053800/b053800.txt">Table of n, a(n) for n = 0..10000</a>
%H A053800 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 A053800 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,4,-4,3,-2,3,-3,1).
%F A053800 G.f.: (1+q)(1+q^2)(1+q^3)(1+q^4)(1+q^5)/((1-q)(1-q^2)(1-q^3)(1-q^4)(1-q^5)).
%F A053800 a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 4*a(n-5) - 4*a(n-6) + 3*a(n-7) - 2*a(n-8) + 3*a(n-9) - 3*a(n-10) + a(n-11) for n>11. - _Colin Barker_, Jan 01 2020
%o A053800 (PARI) Vec((1 + x)*(1 - x + x^2)*(1 - x + x^2 - x^3 + x^4)*(1 + x^4) / ((1 - x)^5*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^45)) \\ _Colin Barker_, Jan 01 2020
%K A053800 easy,nonn
%O A053800 0,2
%A A053800 _James Sellers_, Mar 27 2000