A053798 Number of basis partitions of n+16 with Durfee square size 4.

1, 2, 4, 8, 14, 22, 34, 50, 70, 96, 128, 166, 212, 266, 328, 400, 482, 574, 678, 794, 922, 1064, 1220, 1390, 1576, 1778, 1996, 2232, 2486, 2758, 3050, 3362, 3694, 4048, 4424, 4822, 5244, 5690, 6160, 6656, 7178, 7726, 8302, 8906, 9538, 10200, 10892, 11614

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,-3,3,-1)

Formula

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

a(n) = (n*(n^2+15)+2*A049347(n-1))/9, n>0. G.f. 1+ 2*x*(1-x+x^2-x^3+x^4) / ( (1+x+x^2)*(x-1)^4 ). - R. J. Mathar, Mar 24 2011

Mathematica

LinearRecurrence[{3, -3, 2, -3, 3, -1}, {1, 2, 4, 8, 14, 22, 34}, 50] (* Harvey P. Dale, Dec 29 2019 *)

Crossrefs

Sequence in context: A090533 A025003 A087151 * A305497 A231429 A259392

Adjacent sequences: A053795 A053796 A053797 * A053799 A053800 A053801

Keyword

easy,nonn

Author

James A. Sellers, Mar 27 2000

Status

approved