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A123947
Expansion of x^2*(1+x-x^2)/(1-2*x-4*x^2+x^3+x^4).
1
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
1,3
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 *)
PROG
(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
(Magma) R<x>:=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
(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
(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
CROSSREFS
Sequence in context: A351797 A134325 A220950 * A262253 A303546 A135142
KEYWORD
nonn
AUTHOR
STATUS
approved