A029075 Expansion of 1/((1-x)*(1-x^4)*(1-x^7)*(1-x^10)).

1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 7, 7, 9, 10, 11, 12, 14, 15, 17, 19, 21, 22, 25, 27, 29, 31, 35, 37, 40, 43, 47, 49, 53, 57, 61, 64, 69, 73, 78, 82, 88, 92, 98, 103, 109, 114, 121, 127, 134, 140, 148, 154, 162, 169

Offset

0,5

Comments

Number of partitions of n into parts 1, 4, 7 and 10. - Ilya Gutkovskiy, May 18 2017

Links

Table of n, a(n) for n=0..55.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1,0,1,-1,0,1,-2,1,0,-1,1,0,-1,1,0,0,1,-1).

Formula

a(n) = floor((n^3 + 33*n^2 + 311*n + 1776)/1680 + (n/80)*[(n mod 2)=0] + (1/7)*([(n mod 7)=0] - [(n mod 7)=6])). - Hoang Xuan Thanh, Jul 07 2025

Mathematica

CoefficientList[Series[1/((1-x)(1-x^4)(1-x^7)(1-x^10)), {x, 0, 60}], x] (* Harvey P. Dale, Mar 06 2017 *)
(* Alternative: *)
LinearRecurrence[{1, 0, 0, 1, -1, 0, 1, -1, 0, 1, -2, 1, 0, -1, 1, 0, -1, 1, 0, 0, 1, -1}, {1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 7, 7, 9, 10, 11, 12, 14, 15, 17, 19}, 60] (* Harvey P. Dale, Mar 06 2017 *)

Crossrefs

Sequence in context: A051059 A132968 A132967 * A029052 A131795 A035382

Adjacent sequences: A029072 A029073 A029074 * A029076 A029077 A029078

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved