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A053802
Number of basis partitions of n+49 with Durfee square size 7.
2
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
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
KEYWORD
easy,nonn
AUTHOR
James A. Sellers, Mar 27 2000
STATUS
approved