A029016 Expansion of 1/((1-x)(1-x^2)(1-x^5)(1-x^12)).

1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 18, 20, 23, 26, 29, 32, 36, 39, 44, 47, 53, 57, 63, 68, 74, 80, 87, 93, 101, 107, 116, 123, 133, 141, 151, 160, 171, 181, 193, 203, 216, 227, 241, 253, 268, 281, 297, 311

Offset

0,3

Comments

Number of partitions of n into parts 1, 2, 5, and 12. - Joerg Arndt, May 20 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Maple

M := Matrix(20, (i, j)-> if (i=j-1) or (j=1 and member(i, [1, 2, 5, 8, 12, 15, 18, 19])) then 1 elif j=1 and member(i, [3, 6, 7, 13, 14, 17, 20]) then -1 else 0 fi); a := n -> (M^(n))[1, 1]; seq (a(n), n=0..51); # Alois P. Heinz, Jul 25 2008

Mathematica

s = 1/((1-x)(1-x^2)(1-x^5)(1-x^12)) + O[x]^100; CoefficientList[s, x] (* Jean-François Alcover, Nov 05 2015 *)
LinearRecurrence[{1, 1, -1, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, -1, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 18, 20, 23, 26, 29, 32}, 80] (* Harvey P. Dale, Jun 22 2017 *)

Prog

(PARI) a(n)=floor((2*n^3+60*n^2+513*n+1773)/1440+(n+1)*(-1)^n/96+[0, -1, 0, 1, 0, 2][n%6+1]*(-1)^(n\6)/6) \\ Tani Akinari, May 19 2014

Crossrefs

Sequence in context: A062420 A089197 A017874 * A290807 A121385 A029015

Adjacent sequences: A029013 A029014 A029015 * A029017 A029018 A029019

Keyword

nonn

Author

N. J. A. Sloane

Status

approved