A025871 Expansion of 1/((1-x^4)*(1-x^7)*(1-x^12)).

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 1, 1, 2, 0, 1, 2, 2, 1, 1, 2, 3, 1, 2, 2, 4, 1, 2, 3, 4, 2, 2, 4, 5, 2, 3, 4, 6, 2, 4, 5, 6, 3, 4, 6, 7, 4, 5, 6, 8, 4, 6, 7, 9, 5, 6, 8, 10, 6, 7, 9, 11, 6, 8, 10, 12, 7, 9, 11, 13, 8, 10, 12, 14

Offset

0,13

Comments

Number of partitions of n into parts 4, 7, and 12. - Hoang Xuan Thanh, Sep 13 2025

Links

Table of n, a(n) for n=0..76.

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

Formula

a(n) = a(n-4)+a(n-7)-a(n-11)+a(n-12)-a(n-16)-a(n-19)+a(n-23) with a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=0, a(6)=0, a(7)=1, a(8)=1, a(9)=0, a(10)=0, a(11)=1, a(12)=2, a(13)=0, a(14)=1, a(15)=1, a(16)=2, a(17)=0, a(18)=1, a(19)=2, a(20)=2, a(21)=1, a(22)=1. - Harvey P. Dale, Feb 07 2015

a(n) = floor((n+1)^2/672 + (n+7)*((n+3) mod 4)/48 + (((2*n+2)^2) mod 7)/7). - Hoang Xuan Thanh, Sep 13 2025

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^12)), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 1, 1, 2, 0, 1, 2, 2, 1, 1}, 100] (* Harvey P. Dale, Feb 07 2015 *)

Crossrefs

Sequence in context: A128186 A048823 A173655 * A051010 A328342 A214269

Adjacent sequences: A025868 A025869 A025870 * A025872 A025873 A025874

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved