A117791 Expansion of 1/(1 - x - x^2 + x^4 - x^6).

1, 1, 2, 3, 4, 6, 9, 13, 20, 30, 45, 68, 102, 153, 230, 345, 518, 778, 1168, 1754, 2634, 3955, 5939, 8918, 13391, 20108, 30194, 45339, 68081, 102230, 153508, 230507, 346128, 519744, 780445, 1171912, 1759737, 2642412, 3967832, 5958076, 8946616, 13434192

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = a(n-1) + a(n-2) - a(n-4) + a(n-6). - Ilya Gutkovskiy, Nov 16 2016

Maple

seq(coeff(series(1/(1 -x -x^2 +x^4 -x^6), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 05 2019

Mathematica

CoefficientList[Series[1/(1 -x -x^2 +x^4 -x^6), {x, 0, 50}], x]

Prog

(PARI) Vec(1/(1 -x -x^2 +x^4 -x^6)+O(x^50)) \\ Charles R Greathouse IV, Sep 23 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1-x-x^2+x^4-x^6))); // G. C. Greubel, Nov 03 2018
(Sage)
def A117791_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1 -x -x^2 +x^4 -x^6) ).list()
A117791_list(50) # G. C. Greubel, Dec 05 2019

Crossrefs

Cf. A029826, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A078932 A206740 A172161 * A022860 A022859 A352039

Adjacent sequences: A117788 A117789 A117790 * A117792 A117793 A117794

Keyword

nonn,easy

Author

Roger L. Bagula, Apr 15 2006

Extensions

Edited by N. J. A. Sloane, Nov 08 2006

Status

approved