A078066 Expansion of (1-x)/(1+2*x+x^2+2*x^3).

1, -3, 5, -9, 19, -39, 77, -153, 307, -615, 1229, -2457, 4915, -9831, 19661, -39321, 78643, -157287, 314573, -629145, 1258291, -2516583, 5033165, -10066329, 20132659, -40265319, 80530637, -161061273, 322122547, -644245095, 1288490189, -2576980377, 5153960755, -10307921511

Offset

0,2

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (-2, -1, -2).

Formula

a(n)=(-1)^n*(J(n+1)+2*sum{k=0..floor((n-1)/2), (-1)^k*J(n-2k)}) where J(n)=A001045(n); - Paul Barry, Oct 12 2007

a(0)=1, a(1)=-3, a(2)=5, a(n)=-2*a(n-1)-a(n-2)-2*a(n-3). - Harvey P. Dale, Aug 21 2013

Mathematica

CoefficientList[Series[(1-x)/(1+2x+x^2+2x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{-2, -1, -2}, {1, -3, 5}, 40] (* Harvey P. Dale, Aug 21 2013 *)

Prog

(PARI) Vec((1-x)/(1+2*x+x^2+2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Crossrefs

Sequence in context: A339916 A071384 A291398 * A018002 A255822 A227234

Adjacent sequences: A078063 A078064 A078065 * A078067 A078068 A078069

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved