A029030 Expansion of 1/((1-x)(1-x^2)(1-x^10)(1-x^11)).

1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 54, 57, 63, 67, 73, 77, 83, 87, 93, 97, 104, 109, 117, 123, 132, 138, 147, 153, 162, 168, 178, 185, 196, 204

Offset

0,3

Comments

a(n) is the number of partitions of n into parts 1, 2, 10, and 11. - Joerg Arndt, May 13 2017

Links

Matthew House, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,0,0,0,0,1,0,-2,0,1,0,0,0,0,0,0,-1,1,1,-1).

Formula

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-10) - 2*a(n-12) + a(n-14) - a(n-21) + a(n-22) + a(n-23) - a(n-24). - Matthew House, May 07 2017

a(n) = n^3/1320 + 3/110*n^2 + O(n). - Charles R Greathouse IV, Jun 02 2026

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^10)(1-x^11)), {x, 0, 60}], x] (* Harvey P. Dale, Mar 13 2013 *)

Prog

(PARI) Vec(1/((1-x)*(1-x^2)*(1-x^10)*(1-x^11))+O(x^99)) \\ Charles R Greathouse IV, Jun 02 2026

Crossrefs

Sequence in context: A122522 A227614 A236473 * A008719 A079685 A112409

Adjacent sequences: A029027 A029028 A029029 * A029031 A029032 A029033

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved