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Number of basis partitions of n+25 with Durfee square size 5.
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%I #16 Jan 01 2020 14:10:54

%S 1,2,4,8,14,24,38,58,86,124,174,238,320,422,548,702,886,1106,1366,

%T 1670,2024,2432,2900,3434,4040,4724,5492,6352,7310,8374,9552,10850,

%U 12278,13844,15556,17424,19456,21662,24052,26636,29424,32426,35654,39118

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

%H Seiichi Manyama, <a href="/A053800/b053800.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_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,4,-4,3,-2,3,-3,1).

%F 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 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 (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 easy,nonn

%O 0,2

%A _James A. Sellers_, Mar 27 2000