A029008 Expansion of 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^7)).

1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 14, 16, 20, 22, 27, 30, 36, 39, 46, 50, 58, 63, 72, 78, 88, 95, 106, 114, 127, 136, 150, 160, 176, 187, 204, 217, 236, 250, 270, 286, 308, 325, 349, 368, 394, 414, 442, 464, 494, 518

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 4 and 7. - Ilya Gutkovskiy, May 13 2017

Links

Table of n, a(n) for n=0..49.

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

Formula

a(n) = a(n-1)+a(n-2)-a(n-3)+a(n-4)-a(n-5)-a(n-6)+2*a(n-7)-a(n-8)-a(n-9)+a(n-10)-a(n-11)+a(n-12)+a(n-13)-a(n-14). - Wesley Ivan Hurt, May 27 2021

a(n) = floor((n^3 + 21n^2 + 119n + 384)/336 + n*[n mod 2=0]/16). - Hoang Xuan Thanh, Jul 02 2025

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^4)(1-x^7)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 1, -1, 1, -1, -1, 2, -1, -1, 1, -1, 1, 1, -1}, {1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 14, 16, 20, 22}, 60] (* Harvey P. Dale, Aug 11 2023 *)

Crossrefs

Sequence in context: A322369 A319402 A319403 * A240844 A136343 A161254

Adjacent sequences: A029005 A029006 A029007 * A029009 A029010 A029011

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved