A129920 Expansion of -1/(1 - x + 3*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6).

-1, -1, 2, 3, -4, -10, 5, 29, 2, -76, -45, 178, 212, -361, -750, 565, 2282, -306, -6206, -2428, 15176, 14353, -32719, -55104, 57933, 176234, -61524, -499047, -97429, 1271400, 921652, -2887641, -3948938, 5590078, 13380187, -7828378, -39536779, 108416, 104810904

Offset: 0

Author

Roger L. Bagula, Jun 05 2007

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-3,2,-1,2,-1).

Crossrefs

Cf. A008620, A010892, A014019, A099443, A099479, A099480, A112712.

Cf. A125629, A129704, A129903.

Programs

Magma

R:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( -1/(1-x+3*x^2-2*x^3+x^4-2*x^5+x^6) )); // G. C. Greubel, Sep 28 2024

Mathematica

CoefficientList[Series[-1/(1-x +3*x^2 -2*x^3 +x^4 -2*x^5 +x^6), {x,0,50}], x]

SageMath

def A129920_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( -1/(1-x+3*x^2-2*x^3+x^4-2*x^5+x^6) ).list()
A129920_list(50) # G. C. Greubel, Sep 28 2024

Formula

a(n) = a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6), n >= 6. - Franck Maminirina Ramaharo, Jan 08 2019

Extensions

Edited by Franck Maminirina Ramaharo, Jan 08 2019