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%I #15 Sep 08 2022 08:45:28
%S 0,0,1,0,-2,-2,4,8,-4,-24,-8,56,64,-96,-240,64,672,352,-1472,-2048,
%T 2240,7040,-384,-18560,-13312,37888,63744,-49152,-203264,-29184,
%U 504832,464896,-951296,-1939456,972800,5781504,1933312,-13508608,-15429632,23150592,57876480,-15441920,-162054144,-84869120
%N Expansion of x^3 / ( 1+2*x^2+2*x^3 ).
%C Apart from the offset, the same as A077968.
%H G. C. Greubel, <a href="/A123958/b123958.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,-2,-2).
%t M = {{0, 1, 0}, {0, 0, 1}, {-2, -2, 0}}; v[1] = {0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
%t LinearRecurrence[{0,-2,-2}, {0,0,1}, 50] (* _G. C. Greubel_, Jun 24 2019 *)
%o (PARI) my(x='x+O('x^50)); concat([0,0], Vec( x^3/(1+2*x^2+2*x^3) )) \\ _G. C. Greubel_, Jun 24 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); [0,0] cat Coefficients(R!( x^3/(1+2*x^2+2*x^3) )); // _G. C. Greubel_, Jun 24 2019
%o (Sage) a=(x^3/(1+2*x^2+2*x^3)).series(x, 50).coefficients(x, sparse=False); a[1:] # _G. C. Greubel_, Jun 24 2019
%o (GAP) a:=[0,0,1];; for n in [4..50] do a[n]:=-2*(a[n-2]+a[n-3]); od; a; # _G. C. Greubel_, Jun 24 2019
%Y Cf. A077968.
%K sign,easy
%O 1,5
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 27 2006
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