A077870 Expansion of (1-x)^(-1)/(1-x+2*x^3).

1, 2, 3, 2, -1, -6, -9, -6, 7, 26, 39, 26, -25, -102, -153, -102, 103, 410, 615, 410, -409, -1638, -2457, -1638, 1639, 6554, 9831, 6554, -6553, -26214, -39321, -26214, 26215, 104858, 157287, 104858, -104857, -419430, -629145, -419430, 419431, 1677722, 2516583, 1677722, -1677721, -6710886

Offset

0,2

Links

Table of n, a(n) for n=0..45.

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

Formula

G.f.: G(0)/(1 + x) where G(k) = 1 + 8*x + 2*k*x + k - 2*x*(k+1)*(k+5)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Apr 09 2013

G.f.: G(0)/(2*(1-x^2)*(1-x)), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+2) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 25 2013

a(n) = Sum_{k=0..floor((n+1)/2)} (-2)^k*binomial(n+1-2k,k+1), n>=0. - Taras Goy, Apr 15 2020

Mathematica

LinearRecurrence[{2, -1, -2, 2}, {1, 2, 3, 2}, 50] (* Harvey P. Dale, Jul 28 2019 *)

Crossrefs

Sequence in context: A065369 A336404 A167772 * A294408 A358605 A360026

Adjacent sequences: A077867 A077868 A077869 * A077871 A077872 A077873

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved