A053802 Number of basis partitions of n+49 with Durfee square size 7.

1, 2, 4, 8, 14, 24, 40, 64, 98, 148, 218, 314, 446, 622, 854, 1158, 1550, 2050, 2684, 3478, 4464, 5682, 7172, 8982, 11170, 13796, 16928, 20648, 25040, 30198, 36234, 43262, 51410, 60824, 71656, 84074, 98266, 114430, 132780, 153556, 177008

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 (1,1,0,0,-1,0,-1,-1,0,1,1,2,0,0,0,-2,-1,-1,0,1,1,0,1,0,0,-1,-1,1).

Formula

G.f.: (1+q)(1+q^2)(1+q^3)(1+q^4)(1+q^5)(1+q^6)(1+q^7)/((1-q)(1-q^2)(1-q^3)(1-q^4)(1-q^5)(1-q^6)(1-q^7)).

a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) - a(n-8) + a(n-10) + a(n-11) + 2*a(n-12) - 2*a(n-16) - a(n-17) - a(n-18) + a(n-20) + a(n-21) + a(n-23) - a(n-26) - a(n-27) + a(n-28) for n>28. - Colin Barker, Jan 02 2020

Mathematica

CoefficientList[Series[Times@@(1+x^Range[7])/Times@@(1-x^Range[7]), {x, 0, 40}], x] (* Harvey P. Dale, Aug 30 2017 *)

Prog

(PARI) Vec((1+x)*(1+x^2)*(1+x^3)*(1+x^4)*(1+x^5)*(1+x^6)*(1+x^7) / ((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)) + O(x^40)) \\ Colin Barker, Jan 02 2020

Crossrefs

Sequence in context: A060046 A053801 A091778 * A091779 A365666 A090399

Adjacent sequences: A053799 A053800 A053801 * A053803 A053804 A053805

Keyword

easy,nonn

Author

James A. Sellers, Mar 27 2000

Status

approved