A123947 Expansion of x^2*(1+x-x^2)/(1-2*x-4*x^2+x^3+x^4).

0, 1, 3, 9, 29, 90, 284, 890, 2797, 8780, 27574, 86581, 271881, 853732, 2680833, 8418132, 26433983, 83005929, 260648825, 818469251, 2570093890, 8070410030, 25342077544, 79577232067, 249882270390, 784660981474, 2463931734897

Offset: 1

Author

Gary W. Adamson and Roger L. Bagula, Oct 26 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,4,-1,-1).

Crossrefs

Cf. A122773, A122771.

Programs

GAP

a:=[0,1,3,9];; for n in [5..30] do a[n]:=2*a[n-1]+4*a[n-2]-a[n-3] -a[n-4]; od; a; # G. C. Greubel, Aug 05 2019

Magma

R:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x^2*(1+x-x^2)/(1-2*x-4*x^2+x^3+x^4) )); // G. C. Greubel, Aug 05 2019

Maple

seq(coeff(series(x^2*(1+x-x^2)/(1-2*x-4*x^2+x^3+x^4), x, n+1), x, n), n = 1..30); # G. C. Greubel, Aug 05 2019

Mathematica

M = {{0,-1,-1,0,1}, {-1,0,0,0,-1}, {-1,0,1,0,-1}, {0,0,-1,0,0}, {1,-1, -1,0,1}}; v[1] = {0,0,0,0,1}; v[n_]:= v[n] = M.v[n-1]; Table[v[n][[1]], {n, 30}]
CoefficientList[Series[x^2*(1+x-x^2)/(1-2*x-4*x^2+x^3+x^4), {x, 0, 30}], x] (* G. C. Greubel, Aug 05 2019 *)

PARI

my(x='x+O('x^30)); concat([0], Vec(x^2*(1+x-x^2)/(1-2*x-4*x^2+x^3+x^4))) \\ G. C. Greubel, Aug 05 2019

Sage

a=(x^2*(1+x-x^2)/(1-2*x-4*x^2+x^3+x^4)).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Aug 05 2019