A029066 - OEIS

A029066

Expansion of 1/((1-x)*(1-x^4)*(1-x^5)*(1-x^9)).

1, 1, 1, 1, 2, 3, 3, 3, 4, 6, 7, 7, 8, 10, 12, 13, 14, 16, 19, 21, 23, 25, 28, 31, 34, 37, 40, 44, 48, 52, 56, 60, 65, 70, 75, 80, 86, 92, 98, 104, 111, 118, 125, 132, 140, 149, 157, 165, 174, 184, 194, 203, 213, 224, 236

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OFFSET

0,5

COMMENTS

Number of partitions of n into parts 1, 4, 5 and 9. - Ilya Gutkovskiy, May 17 2017

LINKS

Table of n, a(n) for n=0..54.

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

FORMULA

a(n) = floor((2*n^3 + 57*n^2 + 480*n + 72*(-1)^n + 2208)/2160 + (1/5)*([(n mod 5) in {0,4}] - [(n mod 5) in {1,2}])). - Hoang Xuan Thanh, Aug 04 2025

MATHEMATICA

CoefficientList[Series[1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^9)), {x, 0, 50}], x] (* G. C. Greubel, May 17 2017 *)

LinearRecurrence[{1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 1, -1}, {1, 1, 1, 1, 2, 3, 3, 3, 4, 6, 7, 7, 8, 10, 12, 13, 14, 16, 19}, 60] (* Harvey P. Dale, Apr 21 2019 *)

PROG

(PARI) x='x+O('x^50); Vec(1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^9))) \\ G. C. Greubel, May 17 2017

(PARI) a(n) = floor((2*n^3 + 57*n^2 + 480*n + 72*(-1)^n + 2208)/2160 + (1/5)*[1, -1, -1, 0, 1][n%5+1]) \\ Hoang Xuan Thanh, Aug 04 2025

CROSSREFS

Sequence in context: A048460 A351058 A036017 * A174522 A327719 A327716

Adjacent sequences: A029063 A029064 A029065 * A029067 A029068 A029069

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved