A025830 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^8)).

1, 0, 0, 1, 1, 0, 1, 1, 2, 1, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 7, 4, 5, 7, 8, 5, 7, 8, 10, 7, 8, 10, 12, 8, 10, 12, 14, 10, 12, 14, 16, 12, 14, 16, 19, 14, 16, 19, 21, 16, 19, 21, 24, 19, 21, 24, 27, 21, 24, 27, 30, 24

Offset

0,9

Comments

Number of partitions of n into parts 3, 4, and 8. - Hoang Xuan Thanh, Aug 22 2025

Links

Table of n, a(n) for n=0..65.

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

Formula

a(n) = a(n-3)+a(n-4)-a(n-7)+ a(n-8)-a(n-11)-a(n-12)+a(n-15). - Harvey P. Dale, Mar 31 2013

a(n) = floor((n^2 + 6*(n+10)*(1+ ((n+3) mod 4)))/192). - Hoang Xuan Thanh, Aug 22 2025

a(4*n) = A001399(n). - Hoang Xuan Thanh, Aug 25 2025

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^4)(1-x^8)), {x, 0, 70}], x]  (* or *) LinearRecurrence[{0, 0, 1, 1, 0, 0, -1, 1, 0, 0, -1, -1, 0, 0, 1}, {1, 0, 0, 1, 1, 0, 1, 1, 2, 1, 1, 2, 3, 1, 2}, 70] (* Harvey P. Dale, Mar 31 2013 *)

Prog

(PARI) a(n) = (n^2 + 6*(n+10)*(1+ (n+3)%4))\192 \\ Hoang Xuan Thanh, Aug 22 2025

Crossrefs

Sequence in context: A309014 A070990 A097868 * A389613 A083796 A037039

Adjacent sequences: A025827 A025828 A025829 * A025831 A025832 A025833

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved