A029100 - OEIS

A029100

Expansion of 1/((1-x)*(1-x^5)*(1-x^9)*(1-x^10)).

1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 5, 5, 5, 5, 6, 8, 8, 8, 9, 11, 14, 14, 14, 15, 17, 20, 20, 21, 23, 26, 30, 30, 31, 33, 36, 40, 41, 43, 46, 50, 55, 56, 58, 61, 65, 71, 73, 76, 80, 85, 92, 94, 97, 101, 107, 115, 118, 122, 127

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OFFSET

0,6

COMMENTS

Number of partitions of n into parts 1, 5, 9 and 10. - Ilya Gutkovskiy, May 21 2017

LINKS

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

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

FORMULA

a(n) = floor(n^3/2700 + n^2/72 + 121*n/900 + 65/48 + (n/50)*((3*n^2+3) mod 5) +(-1)^floor(n/5)*(5-2*(n mod 5))/16 + (144*(n mod 5)^3-405*(n mod 5)^2-1575*(n mod 5))/5400). - Hoang Xuan Thanh, Mar 12 2026

MATHEMATICA

CoefficientList[Series[1/((1-x)*(1-x^5)*(1-x^9)*(1-x^10)), {x, 0, 60}], x] (* Hoang Xuan Thanh, Jul 25 2025 *)

PROG

(PARI) a(n) = floor((2*n^3 + 75*n^2 + 834*n + 5625)/5400 + (n/50) * [2, 0, -1, -1, 0][n%5+1] + (1/15) * [10, 5, -1, -5, -5, 0, 0, -5, -5, 0][n%10+1]) \\ Hoang Xuan Thanh, Jul 25 2025

CROSSREFS

Sequence in context: A114869 A316899 A352828 * A356758 A098133 A138185

Adjacent sequences: A029097 A029098 A029099 * A029101 A029102 A029103

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved