A025914 Expansion of 1/((1-x^7)*(1-x^9)*(1-x^12)).

1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 2, 0, 1, 1, 1, 1, 1, 2, 0, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 2, 4, 3, 3, 4, 3, 3, 4, 4, 3, 5, 4, 3, 5, 4, 4, 5, 5, 4, 6, 5, 4, 6, 5, 5, 6, 6

Offset

0,22

Comments

Number of partitions of n into parts 7, 9, and 12. - Hoang Xuan Thanh, Sep 26 2025

Links

Table of n, a(n) for n=0..79.

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

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=1, a(8)=0, a(9)=1, a(10)=0, a(11)=0, a(12)=1, a(13)=0, a(14)=1, a(15)=0, a(16)=1, a(17)=0, a(18)=1, a(19)=1, a(20)=0, a(21)=2, a(22)=0, a(23)=1, a(24)=1, a(25)=1, a(26)=1, a(27)=1, a(n)=a(n-7)+a(n-9)+a(n-12)-a(n-16)-a(n-19)-a(n-21)+a(n-28). - Harvey P. Dale, Dec 19 2012

a(n) = floor((n^2+42*n+405)/1512 - (n+10)*(n mod 3)/108 + ((n^2+6) mod 7)/7). - Hoang Xuan Thanh, Sep 26 2025

Mathematica

CoefficientList[ Series[1/((1-x^7)(1-x^9)(1-x^12)), {x, 0, 120}], x] (* or *)
LinearRecurrence[ {0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 2, 0, 1, 1, 1, 1, 1}, 121] (* Harvey P. Dale, Dec 19 2012 *)

Prog

(PARI) a(n) = (n^2+42*n+405 - 14*(n+10)*(n%3) + 216*((n^2+6)%7))\1512 \\ Hoang Xuan Thanh, Sep 26 2025

Crossrefs

Sequence in context: A070200 A359833 A383210 * A376631 A284977 A025916

Adjacent sequences: A025911 A025912 A025913 * A025915 A025916 A025917

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved