A029285 Expansion of 1/((1-x^3)(1-x^5)(1-x^8)(1-x^12)).

1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 3, 5, 5, 4, 6, 7, 6, 7, 8, 8, 9, 10, 9, 12, 12, 11, 14, 15, 14, 16, 17, 18, 19, 20, 20, 23, 24, 23, 26, 29, 27, 30, 32, 32, 35, 36, 36, 41, 41, 41, 45, 48, 47, 50, 53, 54

Offset

0,9

Comments

Number of partitions of n into parts 3, 5, 8, and 12. - Vincenzo Librandi, Jun 04 2014

Links

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

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].

Index entries for sequences related to Gijswijt's sequence

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

Maple

M:= Matrix(28, (i, j)->
    `if`(i=j-1 or j=1 and i in [3, 5, 12, 16, 23, 25], 1,
    `if`(j=1 and i in [11, 13, 15, 17, 28], -1, 0))):
a:= n-> (M^(n))[1, 1]:
seq(a(n), n=0..70);  # Alois P. Heinz, Jul 25 2008

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^5)(1-x^8)(1-x^12)), {x, 0, 80}], x]  (* Harvey P. Dale, Mar 27 2011 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^5)*(1-x^8)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A190353 A331904 A025829 * A134337 A261733 A268341

Adjacent sequences: A029282 A029283 A029284 * A029286 A029287 A029288

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved