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A077950 Expansion of 1/(1-x+2*x^3). 3
1, 1, 1, -1, -3, -5, -3, 3, 13, 19, 13, -13, -51, -77, -51, 51, 205, 307, 205, -205, -819, -1229, -819, 819, 3277, 4915, 3277, -3277, -13107, -19661, -13107, 13107, 52429, 78643, 52429, -52429, -209715, -314573, -209715, 209715, 838861, 1258291, 838861, -838861, -3355443, -5033165, -3355443 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..46.

Index entries for linear recurrences with constant coefficients, signature (1, 0, -2).

FORMULA

a(n+3)=a(n+2)-2*a(n); a(0)=1,a(1)=1,a(2)=1. - Sergei N. Gladkovskii, Aug 21 2012

a(n) = (-1)^n * A077973(n). - Ralf Stephan, Aug 18 2013

G.f.: G(0)/(2*(1-x^2)), 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(0)=1, a(1)=1, a(2)=1, a(n)=a(n-1)-2*a(n-3). - Harvey P. Dale, Oct 18 2013

MATHEMATICA

CoefficientList[Series[1/(1-x+2x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[ {1, 0, -2}, {1, 1, 1}, 50] (* Harvey P. Dale, Oct 18 2013 *)

PROG

(PARI) Vec(1/(1-x+2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

Sequence in context: A133773 A077934 * A077973 A210606 A254327 A175999

Adjacent sequences:  A077947 A077948 A077949 * A077951 A077952 A077953

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002, Jun 17 2007

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)