A029001 Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^7)).

1, 1, 2, 3, 4, 5, 7, 9, 11, 14, 17, 20, 24, 28, 33, 38, 44, 50, 57, 64, 72, 81, 90, 100, 111, 122, 134, 147, 161, 175, 191, 207, 224, 242, 261, 281, 302, 324, 347, 371, 396, 422, 450, 478, 508, 539, 571, 604, 639

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of partitions of n into parts 1, 2, 3, and 7. [Joerg Arndt, Jul 06 2013]

Links

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

Programs

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^3)(1-x^7)),{x,0,50}],x] (* or *) LinearRecurrence[{1,1,0,-1,-1,1,1,-1,-1,0,1,1,-1},{1,1,2,3,4,5,7,9,11,14,17,20,24},50] (* Harvey P. Dale, Nov 13 2013 *)

PARI

Vec(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^7))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Formula

a(n) = floor((n+12)*(2*n^2+15*n+42)/504). - Tani Akinari, Jul 06 2013

a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=7, a(7)=9, a(8)=11, a(9)=14, a(10)=17, a(11)=20, a(12)=24, a(n)=a(n-1)+a(n-2)-a(n-4)- a(n-5)+ a(n-6)+a(n-7)-a(n-8)-a(n-9)+a(n-11)+a(n-12)-a(n-13). - Harvey P. Dale, Nov 13 2013