A029068 Expansion of 1/((1-x)*(1-x^4)*(1-x^5)*(1-x^11)).

1, 1, 1, 1, 2, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 21, 23, 25, 27, 30, 33, 36, 39, 42, 45, 49, 53, 57, 61, 65, 70, 75, 80, 85, 90, 96, 102, 108, 114, 121, 128, 135, 142, 150, 158, 166, 174, 183, 192, 201

Offset

0,5

Comments

Number of partitions of n into parts 1, 4, 5 and 11. - Ilya Gutkovskiy, May 17 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = floor((2*n^3 + 63*n^2 + 580*n + 88*(-1)^n + 2760)/2640 + (1/5)*((-1)^[(n mod 5)>1] + [(n mod 5)=2])). - Hoang Xuan Thanh, Aug 06 2025

Mathematica

CoefficientList[Series[1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^11)), {x, 0, 50}], x] (* G. C. Greubel, May 17 2017 *)

Prog

(PARI) my(x='x+O('x^50)); Vec(1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^11))) \\ G. C. Greubel, May 17 2017
(PARI) a(n) = floor((2*n^3 + 63*n^2 + 580*n + 88*(-1)^n + 2760)/2640 + (1/5)*[1, 1, 0, -1, -1][n%5+1]) \\ Hoang Xuan Thanh, Aug 06 2025

Crossrefs

Sequence in context: A275890 A029087 A177497 * A108932 A029067 A048460

Adjacent sequences: A029065 A029066 A029067 * A029069 A029070 A029071

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved