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

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

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,-3,2,-3,4,-4,3,-2,3,-3,1).

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

Adjacent sequences: A053797 A053798 A053799 * A053801 A053802 A053803

Keyword

easy,nonn

Author

James A. Sellers, Mar 27 2000

Status

approved