A029310 Expansion of 1/((1-x^3)*(1-x^7)*(1-x^9)*(1-x^10)).

1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 1, 2, 3, 2, 3, 4, 3, 4, 4, 4, 5, 5, 5, 7, 7, 6, 9, 8, 7, 10, 10, 9, 12, 13, 11, 14, 15, 13, 16, 17, 16, 19, 20, 19, 22, 23, 22, 25, 26, 25, 29, 30, 29, 33, 34, 33, 37, 38, 37, 42, 43, 42

Offset

0,10

Comments

Number of partitions of n into parts 3, 7, 9, and 10. - Hoang Xuan Thanh, Apr 09 2026

Links

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

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

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=0, a(5)=0, a(6)=1, a(7)=1, a(8)=0, a(9)=2, a(10)=2, a(11)=0, a(12)=2, a(13)=2, a(14)=1, a(15)=2, a(16)=3, a(17)=2, a(18)=3, a(19)=4, a(20)=3, a(21)=4, a(22)=4, a(23)=4, a(24)=5, a(25)=5, a(26)=5, a(27)=7, a(28)=7, a(n)=a(n-3)+a(n-7)+a(n-9)- a(n-12)-a(n-13)- a(n-16)-a(n-17)+a(n-20)+a(n-22)+a(n-26)-a(n-29). - Harvey P. Dale, Sep 09 2015

a(n) = floor((2*n^3+87*n^2+1422*n+14240)/22680 - ((2*n^2+n) mod 3)*n/27 - (n mod 3)/3 + ((2*n^2+1) mod 3)/9 + ((2*n^3+3*n^2+n+2) mod 7)/7 + ([(n mod 9)=1] - [(n mod 9)=6])/3). - Hoang Xuan Thanh, Apr 09 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^7)(1-x^9)(1-x^10)), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, -1, -1, 0, 0, -1, -1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, -1}, {1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 1, 2, 3, 2, 3, 4, 3, 4, 4, 4, 5, 5, 5, 7, 7}, 70] (* Harvey P. Dale, Sep 09 2015 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^7)*(1-x^9)*(1-x^10)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 09 2026

Crossrefs

Sequence in context: A111165 A349812 A029321 * A348220 A134131 A378225

Adjacent sequences: A029307 A029308 A029309 * A029311 A029312 A029313

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved