A053801 Number of basis partitions of n+36 with Durfee square size 6.
1, 2, 4, 8, 14, 24, 40, 62, 94, 140, 202, 286, 398, 542, 728, 966, 1262, 1630, 2084, 2634, 3300, 4100, 5048, 6170, 7490, 9028, 10816, 12884, 15258, 17978, 21082, 24602, 28586, 33080, 38124, 43776, 50090, 57114, 64916, 73560, 83104, 93626
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000
- M. D. Hirschhorn, Basis partitions and Rogers-Ramanujan partitions, Discrete Math. 205 (1999), 241-243.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-6,7,-6,6,-6,7,-6,3,-3,3,-1).
Programs
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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 */ -
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
Formula
Euler transform of length 12 sequence [ 2, 1, 2, 1, 2, 1, 0, -1, 0, -1, 0, -1]. - Michael Somos, Sep 02 2006
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)).
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