A029183 Expansion of 1/((1-x^2)*(1-x^4)*(1-x^7)*(1-x^10)).

1, 0, 1, 0, 2, 0, 2, 1, 3, 1, 4, 2, 5, 2, 7, 3, 8, 4, 10, 5, 12, 7, 14, 8, 17, 10, 19, 12, 23, 14, 26, 17, 30, 19, 34, 23, 38, 26, 43, 30, 48, 34, 54, 38, 60, 43, 66, 48, 73, 54, 80, 60, 88, 66, 96, 73, 105, 80, 114, 88, 124

Offset

0,5

Comments

a(n) is the number of partitions of n into parts 2, 4, 7, and 10. - Hoang Xuan Thanh, Oct 11 2025

Links

Table of n, a(n) for n=0..60.

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

Formula

G.f.: 1/((1-x^2)*(1-x^4)*(1-x^7)*(1-x^10)).

a(n) = a(n-2) + a(n-4) - a(n-6) + a(n-7) - a(n-9) + a(n-10) - a(n-11) - a(n-12) + a(n-13) - a(n-14) + a(n-16) - a(n-17) + a(n-19) + a(n-21) - a(n-23). - Wesley Ivan Hurt, Jun 26 2025

a(n) = floor((n^3+45*n^2+596*n+2112)/3360 - (n^2+23*n+96)*(n mod 2)/160 + ((5*n^3+n^2+5*n+4) mod 7)/7). - Hoang Xuan Thanh, Oct 11 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^7)(1-x^10)), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 0, 1, 0, -1, 1, 0, -1, 1, -1, -1, 1, -1, 0, 1, -1, 0, 1, 0, 1, 0, -1}, {1, 0, 1, 0, 2, 0, 2, 1, 3, 1, 4, 2, 5, 2, 7, 3, 8, 4, 10, 5, 12, 7, 14}, 70] (* Harvey P. Dale, Apr 11 2018 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^4)*(1-x^7)*(1-x^10)) + O(x^80)) \\ Jinyuan Wang, Feb 28 2020

Crossrefs

Sequence in context: A341976 A029221 A304034 * A391233 A213423 A339374

Adjacent sequences: A029180 A029181 A029182 * A029184 A029185 A029186

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved