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A053800
Number of basis partitions of n+25 with Durfee square size 5.
2
1, 2, 4, 8, 14, 24, 38, 58, 86, 124, 174, 238, 320, 422, 548, 702, 886, 1106, 1366, 1670, 2024, 2432, 2900, 3434, 4040, 4724, 5492, 6352, 7310, 8374, 9552, 10850, 12278, 13844, 15556, 17424, 19456, 21662, 24052, 26636, 29424, 32426, 35654, 39118
OFFSET
0,2
LINKS
M. D. Hirschhorn, Basis partitions and Rogers-Ramanujan partitions, Discrete Math. 205 (1999), 241-243.
FORMULA
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)).
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
PROG
(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
CROSSREFS
Sequence in context: A005598 A290845 A100250 * A262968 A261203 A281968
KEYWORD
easy,nonn
AUTHOR
James A. Sellers, Mar 27 2000
STATUS
approved