A029067 Expansion of 1/((1-x)*(1-x^4)*(1-x^5)*(1-x^10)).

1, 1, 1, 1, 2, 3, 3, 3, 4, 5, 7, 7, 8, 9, 11, 13, 14, 15, 17, 19, 23, 24, 26, 28, 32, 36, 38, 40, 44, 48, 54, 56, 60, 64, 70, 76, 80, 84, 90, 96, 105, 109, 115, 121, 130, 139, 145, 151, 160, 169, 181, 187, 196, 205, 217, 229, 238, 247, 259, 271, 287, 296, 308

Offset

0,5

Comments

Number of partitions of n into parts 1, 4, 5 and 10. - Ilya Gutkovskiy, May 17 2017

Links

Table of n, a(n) for n=0..62.

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

Mathematica

CoefficientList[Series[1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^10)), {x, 0, 50}], x] (* G. C. Greubel, May 17 2017 *)
LinearRecurrence[{1, 0, 0, 1, 0, -1, 0, 0, -1, 2, -1, 0, 0, -1, 0, 1, 0, 0, 1, -1}, {1, 1, 1, 1, 2, 3, 3, 3, 4, 5, 7, 7, 8, 9, 11, 13, 14, 15, 17, 19}, 70] (* Harvey P. Dale, Jan 17 2019 *)

Prog

(PARI) a(n)=round((n+10)*(2*n^2+40*n+129+15*(-1)^n)/2400+(n\5+1)*[2, 0, -1, -1, 0][n%5+1]/10+(n%2)*(-1)^(n\2)/8) \\ Tani Akinari, May 22 2014
(PARI) x='x+O('x^50); Vec(1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^10))) \\ G. C. Greubel, May 17 2017

Crossrefs

Sequence in context: A177497 A029068 A108932 * A048460 A351058 A036017

Adjacent sequences: A029064 A029065 A029066 * A029068 A029069 A029070

Keyword

nonn

Author

N. J. A. Sloane

Status

approved