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

Author

Roger L. Bagula, Apr 15 2006

Keywords

• nonn
• easy

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).

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.

Programs

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1-x-x^2+x^4-x^6))); // G. C. Greubel, Nov 03 2018

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]

PARI

Vec(1/(1 -x -x^2 +x^4 -x^6)+O(x^50)) \\ Charles R Greathouse IV, Sep 23 2012

Sage

def A117791_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1 -x -x^2 +x^4 -x^6) ).list()
A117791_list(50) # G. C. Greubel, Dec 05 2019

Formula

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

Extensions

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