A078006 Expansion of (1-x)/(1-x-2*x^2-2*x^3).

1, 0, 2, 4, 8, 20, 44, 100, 228, 516, 1172, 2660, 6036, 13700, 31092, 70564, 160148, 363460, 824884, 1872100, 4248788, 9642756, 21884532, 49667620, 112722196, 255826500, 580606132, 1317703524, 2990568788, 6787188100, 15403732724, 34959246500, 79341088148, 180067046596

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..999
• Index entries for linear recurrences with constant coefficients, signature (1, 2, 2).

Programs

GAP

a:=[1,0,2];; for n in [4..40] do a[n]:=a[n-1]+2*a[n-2]+2*a[n-3]; od; a; # G. C. Greubel, Jun 27 2019

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-x-2*x^2-2*x^3) )); // G. C. Greubel, Jun 27 2019

Mathematica

CoefficientList[Series[(1-x)/(1-x-2x^2-2x^3),{x,0,40}],x] (* or *) LinearRecurrence[{1,2,2},{1,0,2},41] (* Harvey P. Dale, Sep 25 2011 *)

PARI

Vec((1-x)/(1-x-2*x^2-2*x^3)+O(x^40)) \\ Charles R Greathouse IV, Sep 27 2012

Sage

((1-x)/(1-x-2*x^2-2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 27 2019

Formula

a(0)=1, a(1)=0, a(2)=2, a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3). - Harvey P. Dale, Sep 25 2011