A077913 - OEIS

A077913

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

1, 0, -1, 1, 2, -2, -2, 5, 2, -9, 1, 16, -8, -24, 25, 32, -57, -31, 114, 6, -202, 77, 322, -273, -447, 672, 496, -1392, -271, 2560, -625, -4223, 2914, 6158, -7762, -7467, 16834, 5863, -32063, 3504, 54760, -29704, -83319, 87968, 108375, -200991, -103726, 397334, 11110, -702051, 282498, 1110495

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OFFSET

0,5

LINKS

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

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

FORMULA

G.f.: 1-x^2/(U(0)+x^2) where U(k)= 1 + (1+x)*x/( 1 - (1+x)*x/((1+x)*x + 1/U(k+1))) ; (continued fraction, 2-step). - Sergei N. Gladkovskii, Oct 24 2012

5*a(n) = 1 + 4*A077979(n) + 3*A077979(n-1) + A077979(n-2). - R. J. Mathar, Jul 10 2013

MATHEMATICA

LinearRecurrence[{0, -1, 1, 1}, {1, 0, -1, 1}, 60] (* or *) CoefficientList[ Series[1/((1-x)*(1+x+2*x^2+x^3)), {x, 0, 60}], x] (* G. C. Greubel, Jul 02 2019 *)

PROG

(PARI) my(x='x+O('x^60)); Vec(1/((1-x)*(1+x+2*x^2+x^3))) \\ G. C. Greubel, Jul 02 2019

(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1-x)*(1+x+2*x^2+x^3)) )); // G. C. Greubel, Jul 02 2019

(Sage) (1/((1-x)*(1+x+2*x^2+x^3))).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Jul 02 2019

(GAP) a:=[1, 0, -1, 1];; for n in [5..60] do a[n]:=-a[n-2]+a[n-3]+a[n-4]; od; a; # G. C. Greubel, Jul 02 2019

CROSSREFS

Sequence in context: A355198 A363924 A029662 * A069862 A075002 A228917

Adjacent sequences: A077910 A077911 A077912 * A077914 A077915 A077916

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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