A077952 Expansion of 1/(1 - x + x^2 + 2*x^3).

1, 1, 0, -3, -5, -2, 9, 21, 16, -23, -81, -90, 37, 289, 432, 69, -941, -1874, -1071, 2685, 7504, 6961, -5913, -27882, -35891, 3817, 95472, 163437, 60331, -294050, -681255, -507867, 761488, 2631865, 2886111, -1268730, -9418571, -13922063, -1966032, 30793173, 60603331, 33742222, -88447455

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Comments

Row sums of Riordan array (1, x*(1-x-2*x^2)). - Paul Barry, Mar 09 2006

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).

Programs

GAP

a:=[1,1,0];; for n in [4..50] do a[n]:=a[n-1]-a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Aug 07 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x+x^2+2*x^3) )); // G. C. Greubel, Aug 07 2019

Maple

seq(coeff(series(1/(1-x+x^2+2*x^3), x, n+1), x, n), n = 0 .. 50); # G. C. Greubel, Aug 07 2019

Mathematica

LinearRecurrence[{1,-1,-2}, {1,1,0}, 50] (* or *) CoefficientList[Series[ 1/(1-x+x^2+2*x^3), {x,0,50}], x] (* G. C. Greubel, Aug 07 2019 *)

PARI

Vec(1/(1-x+x^2+2*x^3)+O(x^50)) \\ Charles R Greathouse IV, Sep 27 2012

Sage

(1/(1-x+x^2+2*x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Aug 07 2019

Formula

a(n) = Sum_{k=0..n} Sum_{j=0..n} C(k,j-k)*C(k,n-j)*(-2)^(n-j). - Paul Barry, Mar 09 2006

a(n) = (-1)^n*A077975(n). - R. J. Mathar, Jul 31 2010