A029144 Expansion of 1/((1-x^2)(1-x^3)(1-x^5)(1-x^7)).

1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 7, 7, 9, 10, 11, 13, 14, 16, 18, 20, 22, 24, 27, 29, 32, 35, 38, 41, 45, 48, 52, 56, 60, 65, 69, 74, 79, 84, 90, 95, 102, 107, 114, 121, 127, 135, 142, 150, 158, 166, 175, 183, 193, 202, 212, 222, 232, 243, 254, 265, 277

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,0,0,-1,-1,0,0,0,0,1,1,0,-1).

Programs

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^5)(1-x^7)),{x,0,60}],x] (* Harvey P. Dale, Oct 28 2011 *)

Maxima

a(n):=floor((2*n^3+51*n^2+390*n+2020)/2520+((-1)^mod(n,5)-floor(mod(n,5)/4))/5); /* Tani Akinari, Nov 13 2012 */

PARI

Vec(1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^7)) + O(x^90)) \\ Jinyuan Wang, Mar 18 2020