A025869 Expansion of 1/((1-x^4)*(1-x^7)*(1-x^10)).

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

Offset

0,15

Comments

Number of partitions of n into parts 4, 7, and 10. - Hoang Xuan Thanh, Sep 10 2025

Links

Table of n, a(n) for n=0..74.

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

Formula

a(n) = a(n-4)+a(n-7)+a(n-10)-a(n-11)-a(n-14)-a(n-17)+a(n-21) 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)=1, a(11)=1, a(12)=1, a(13)=0, a(14)=2, a(15)=1, a(16)=1, a(17)=1, a(18)=2, a(19)=1, a(20)=2. - Harvey P. Dale, May 07 2014

a(n) = floor((n^2 + 21*n + 122)/560 + (n+10)*(-1)^n/80 + ((2*n^2+6) mod 7)/7). - Hoang Xuan Thanh, Sep 10 2025

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^10)), {x, 0, 90}], x] S(* or *)
LinearRecurrence[{0, 0, 0, 1, 0, 0, 1, 0, 0, 1, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 2}, 90] (* Harvey P. Dale, May 07 2014 *)

Prog

(PARI) a(n)=(n^2+21*n+122 + 7*(n+10)*(-1)^n + 80*((2*n^2+6)%7))\560 \\ Hoang Xuan Thanh, Sep 10 2025

Crossrefs

Sequence in context: A363298 A025909 A025899 * A093320 A082370 A005136

Adjacent sequences: A025866 A025867 A025868 * A025870 A025871 A025872

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved