A025911 Expansion of 1/((1-x^7)*(1-x^8)*(1-x^12)).

1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 0, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 1, 2, 2, 3, 1, 2, 3, 3, 2, 2, 3, 4, 2, 3, 3, 4, 2, 3, 4, 5, 3, 3, 4, 5, 3, 4, 5, 6, 3, 4, 5, 6, 4, 5, 6, 7, 4, 5, 6, 7, 5, 6, 7

Offset

0,25

Comments

Number of partitions of n into parts 7, 8, 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 (0,0,0,0,0,0,1,1,0,0,0,1,0,0,-1,0,0,0,-1,-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)=1, a(9)=0, a(10)=0, a(11)=0, a(12)=1, a(13)=0, a(14)=1, a(15)=1, a(16)=1, a(17)=0, a(18)=0, a(19)=1, a(20)=1, a(21)=1, a(22)=1, a(23)=1, a(24)=2, a(25)=0, a(26)=1, a(n)=a(n-7)+a(n-8)+a(n-12)-a(n-15)- a(n-19)- a(n-20)+ a(n-27). - Harvey P. Dale, Mar 30 2014

a(n) = floor((n^2+6*n+534)/1344 + (n+1)*((n+3) mod 4)/96 + ((2*n^2+5*n+4) mod 7)/7). - Hoang Xuan Thanh, Sep 26 2025

Mathematica

CoefficientList[Series[1/((1-x^7)(1-x^8)(1-x^12)), {x, 0, 80}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 0, 1}, 80] (* Harvey P. Dale, Mar 30 2014 *)

Prog

(PARI) a(n) = (n^2+6*n+534 + 14*(n+1)*((n+3)%4) + 192*((2*n^2+5*n+4)%7))\1344 \\ Hoang Xuan Thanh, Sep 26 2025

Crossrefs

Sequence in context: A340453 A116374 A181953 * A060184 A055639 A156542

Adjacent sequences: A025908 A025909 A025910 * A025912 A025913 A025914

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved