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%I #20 Jan 02 2020 08:23:25
%S 1,2,4,8,14,24,40,62,94,140,202,286,398,542,728,966,1262,1630,2084,
%T 2634,3300,4100,5048,6170,7490,9028,10816,12884,15258,17978,21082,
%U 24602,28586,33080,38124,43776,50090,57114,64916,73560,83104,93626
%N Number of basis partitions of n+36 with Durfee square size 6.
%H Seiichi Manyama, <a href="/A053801/b053801.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_14">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,3,-6,7,-6,6,-6,7,-6,3,-3,3,-1).
%F Euler transform of length 12 sequence [ 2, 1, 2, 1, 2, 1, 0, -1, 0, -1, 0, -1]. - _Michael Somos_, Sep 02 2006
%F G.f.: (1+q)(1+q^2)(1+q^3)(1+q^4)(1+q^5)(1+q^6)/((1-q)(1-q^2)(1-q^3)(1-q^4)(1-q^5)(1-q^6)).
%F a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3) - 6*a(n-4) + 7*a(n-5) - 6*a(n-6) + 6*a(n-7) - 6*a(n-8) + 7*a(n-9) - 6*a(n-10) + 3*a(n-11) - 3*a(n-12) + 3*a(n-13) - a(n-14) for n>14. - _Colin Barker_, Jan 02 2020
%o (PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1,6, (1+x^k)/(1-x^k), 1+x*O(x^n)), n))} /* _Michael Somos_, Sep 02 2006 */
%o (PARI) Vec((1 + x^2)*(1 - x + x^2 - x^3 + x^4)*(1 - x^2 + x^4)*(1 + x^4) / ((1 - x)^6*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^50)) \\ _Colin Barker_, Jan 02 2020
%K easy,nonn
%O 0,2
%A _James A. Sellers_, Mar 27 2000
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