A029123 Expansion of 1/((1-x)*(1-x^7)*(1-x^9)*(1-x^12)).

1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 10, 10, 11, 12, 13, 14, 15, 17, 17, 19, 20, 21, 23, 24, 26, 28, 30, 31, 33, 35, 36, 39, 41, 43, 46, 48, 50, 53, 56, 58, 61, 64, 66, 70, 73, 76, 80, 83, 86, 90, 94, 97, 102, 106, 109, 114, 118, 122, 127

Offset

0,8

Comments

Number of partitions of n into parts 1, 7, 9, and 12. - Michel Marcus, Aug 04 2025

Links

Table of n, a(n) for n=0..69.

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

Formula

a(n) = floor((2*n^3 + 87*n^2 + 1152*n + 9127)/9072 - (n/108)*[(n mod 3)=2] + (1/6)*([(n mod 7)=0] - [(n mod 7)in{4,6}])). - Hoang Xuan Thanh, Aug 04 2025

Mathematica

CoefficientList[Series[1/((1-x)(1-x^7)(1-x^9)(1-x^12)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, -1, 0, 0, -1, 1, 0, -1, 1, -1, 1, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 10, 10, 11, 12, 13, 14, 15, 17}, 60] (* Harvey P. Dale, Aug 03 2017 *)

Crossrefs

Sequence in context: A057357 A308358 A229803 * A025777 A269862 A194200

Adjacent sequences: A029120 A029121 A029122 * A029124 A029125 A029126

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

a(61)-a(69) from Hoang Xuan Thanh, Aug 04 2025

Status

approved