A077956 Expansion of 1/(1-x+2*x^2+2*x^3).

1, 1, -1, -5, -5, 7, 27, 23, -45, -145, -101, 279, 771, 415, -1685, -4057, -1517, 9967, 21115, 4215, -57949, -108609, -1141, 331975, 551475, -110193, -1877093, -2759657, 1214915, 10488415, 13577899, -9828761, -57961389, -65459665, 70120635, 316962743, 307640803, -466525953

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(0)=1, a(1)=1, a(2)=-1, a(n) = a(n-1) - 2*a(n-2) - 2*a(n-3). - Harvey P. Dale, Oct 14 2011

a(n) = (-1)^n * A077977(n). - G. C. Greubel, Jul 02 2019

Mathematica

CoefficientList[Series[1/(1-x+2x^2+2x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, -2, -2}, {1, 1, -1}, 40] (* Harvey P. Dale, Oct 14 2011 *)

Prog

(Magma) I:=[1, 1, -1]; [n le 3 select I[n] else Self(n-1)-2*Self(n-2) -2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Sep 09 2016
(PARI) my(x='x+O('x^40)); Vec(1/(1-x+2*x^2+2*x^3)) \\ G. C. Greubel, Jul 02 2019
(Sage) (1/(1-x+2*x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jul 02 2019
(GAP) a:=[1, 1, -1];; for n in [4..40] do a[n]:=a[n-1]-2*a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jul 02 2019

Crossrefs

Cf. A077977.

Sequence in context: A088048 A006146 A284129 * A077977 A019204 A301733

Adjacent sequences: A077953 A077954 A077955 * A077957 A077958 A077959

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved