A001304 Expansion of 1/((1-x)^2*(1-x^2)*(1-x^5)).

1, 2, 4, 6, 9, 13, 18, 24, 31, 39, 49, 60, 73, 87, 103, 121, 141, 163, 187, 213, 242, 273, 307, 343, 382, 424, 469, 517, 568, 622, 680, 741, 806, 874, 946, 1022, 1102, 1186, 1274, 1366, 1463, 1564, 1670, 1780, 1895, 2015, 2140, 2270, 2405, 2545, 2691, 2842

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Ways of making change for n cents using coins of 1, 2 and 5 cents, if two different kinds of 1-cent coin are counted as different. - Matthew Vandermast, Feb 27 2003

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 113, Example (2), D(n; 1,2,4,10).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 198
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1,1,-2,0,2,-1).

Crossrefs

First differences are in A000115.

Programs

Maple

a:= proc(n) local m, r; m:= iquo(n, 10, 'r'); r:= r+1; (53+ (135+ 100*m) *m) *m/6+ [1, 2, 4, 6, 9, 13, 18, 24, 31, 39][r]+ [0, 5, 11, 18, 26, 35, 45, 56, 68, 81][r]*m+ (r-1)*5 *m^2 end: seq(a(n), n=0..100); # Alois P. Heinz, Oct 05 2008

Mathematica

CoefficientList[Series[1/((1-x)^2*(1-x^2)*(1-x^5)),{x,0,50}],x] (* Vincenzo Librandi, Feb 24 2012 *)
LinearRecurrence[{2,0,-2,1,1,-2,0,2,-1},{1,2,4,6,9,13,18,24,31},60] (* Harvey P. Dale, Oct 03 2018 *)

PARI

a(n)=floor((n+8)*(2*n^2+11*n+18)/120) \\ Tani Akinari, May 14 2014

Formula

G.f.: 1/((1-x)^2*(1-x^2)*(1-x^5)) = 1 / ((1+x)*(x^4+x^3+x^2+x+1)*(x-1)^4).

a(n) = floor((n+8)*(2*n^2+11*n+18)/120). - Tani Akinari, May 14 2014