A025864 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^12)).

1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 4, 3, 2, 2, 4, 4, 3, 2, 5, 4, 4, 3, 6, 5, 4, 4, 7, 6, 5, 4, 8, 7, 6, 5, 9, 8, 7, 6, 10, 9, 8, 7, 11, 10, 9, 8, 13, 11, 10, 9, 14, 13, 11, 10, 15, 14, 13, 11, 17, 15

Offset

0,13

Comments

Number of partitions of n into parts 4, 5, and 12. - Hoang Xuan Thanh, Sep 09 2025

Links

Table of n, a(n) for n=0..73.

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

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=1, a(6)=0, a(7)=0, a(8)=1, a(9)=1, a(10)=1, a(11)=0, a(12)=2, a(13)=1, a(14)=1, a(15)=1, a(16)=2, a(17)=2, a(18)=1, a(19)=1, a(20)=3, a(n)=a(n-4)+a(n-5)-a(n-9)+ a(n-12)-a(n-16)- a(n-17)+a(n-21). - Harvey P. Dale, Mar 22 2015

a(n) = floor((n+12)*(n+24)/480 - n*(n mod 4)/48 + ((4*n^2+4*n+2) mod 5)/5). - Hoang Xuan Thanh, Sep 09 2025

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^12)), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 2, 1, 1, 3}, 100] (* Harvey P. Dale, Mar 22 2015 *)

Prog

(PARI) a(n) = ((n+12)*(n+24) - 10*n*(n%4) + 96*((4*n^2+4*n+2)%5))\480 \\ Hoang Xuan Thanh, Sep 09 2025

Crossrefs

Sequence in context: A322871 A322870 A170979 * A070242 A242748 A374163

Adjacent sequences: A025861 A025862 A025863 * A025865 A025866 A025867

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved