A025829 Expansion of 1/((1-x^3)(1-x^4)(1-x^7)).

1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 7, 8, 9, 9, 9, 10, 11, 11, 11, 12, 13, 13, 13, 15, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 30, 30, 30

Offset

0,8

Comments

Partition of n into parts 3, 4, and 7; see A245368 for the compositions. - David Neil McGrath, Sep 08 2014

Links

Robert Israel, Table of n, a(n) for n = 0..10000

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.

Index entries for sequences related to Gijswijt's sequence

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

Formula

a(n) = a(n-3)+a(n-4)-a(n-10)-a(n-11)+a(n-14). - David Neil McGrath, Sep 08 2014

Example

There are 7 partitions of 27 into parts 3,4 and 7. These are (77733)(774333)(744444)(7443333)(4444443)(44433333)(333333333). - David Neil McGrath, Sep 08 2014

Maple

f:= gfun:-rectoproc({a(0) = 1, a(1) = 0, a(2) = 0, a(3) = 1, a(4) = 1, a(5) = 0, a(6) = 1, a(7) = 2, a(8) = 1, a(9) = 1, a(10) = 2, a(11) = 2, a(12) = 2, a(13) = 2, a(n) = a(n-3)+a(n-4)-a(n-10)-a(n-11)+a(n-14)}, a(n), 'remember'):
seq(f(n), n=0..100); # Robert Israel, Sep 08 2014

Mathematica

LinearRecurrence[{0, 0, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1}, {1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 2, 2, 2, 2}, 80] (* Jean-François Alcover, Aug 21 2022 *)

Prog

(PARI) a(n)=floor((-2)^(n%3\2)/9-(n%2)*(-1)^(n\2)/4+(3*n^2+42*n+448)/504) \\ Tani Akinari, Aug 19 2013
(PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^7)) + O(x^80)) \\ Michel Marcus, Sep 08 2014

Crossrefs

Sequence in context: A298604 A190353 A331904 * A029285 A134337 A261733

Adjacent sequences: A025826 A025827 A025828 * A025830 A025831 A025832

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved