A077972 Expansion of 1/(1+x-x^2+2*x^3).

1, -1, 2, -5, 9, -18, 37, -73, 146, -293, 585, -1170, 2341, -4681, 9362, -18725, 37449, -74898, 149797, -299593, 599186, -1198373, 2396745, -4793490, 9586981, -19173961, 38347922, -76695845, 153391689, -306783378, 613566757, -1227133513, 2454267026, -4908534053, 9817068105

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = (-1)^n * A077947(n).

G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1 - x*(4*k+1 - x + 2*x^2 )/( x*(4*k+3 - x + 2*x^2 ) - 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 09 2013

Mathematica

LinearRecurrence[{-1, 1, -2}, {1, -1, 2}, 40] (* or *) CoefficientList[ Series[1/(1+x-x^2+2*x^3), {x, 0, 40}], x] (* G. C. Greubel, Jun 24 2019 *)

Prog

(PARI) Vec(1/(1+x-x^2+2*x^3)+O(x^40)) \\ Charles R Greathouse IV, Sep 27 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1+x-x^2+2*x^3) )); // G. C. Greubel, Jun 24 2019
(Sage) (1/(1+x-x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 24 2019
(GAP) a:=[1, -1, 2];; for n in [4..40] do a[n]:=-a[n-1]+a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jun 24 2019

Crossrefs

Cf. A077947.

Sequence in context: A068036 A364525 A077947 * A293354 A293329 A152546

Adjacent sequences: A077969 A077970 A077971 * A077973 A077974 A077975

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved