A123958 Expansion of x^3 / ( 1+2*x^2+2*x^3 ).

0, 0, 1, 0, -2, -2, 4, 8, -4, -24, -8, 56, 64, -96, -240, 64, 672, 352, -1472, -2048, 2240, 7040, -384, -18560, -13312, 37888, 63744, -49152, -203264, -29184, 504832, 464896, -951296, -1939456, 972800, 5781504, 1933312, -13508608, -15429632, 23150592, 57876480, -15441920, -162054144, -84869120

Offset

1,5

Comments

Apart from the offset, the same as A077968.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,-2,-2).

Mathematica

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}]
LinearRecurrence[{0, -2, -2}, {0, 0, 1}, 50] (* G. C. Greubel, Jun 24 2019 *)

Prog

(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
(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
(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
(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

Crossrefs

Cf. A077968.

Sequence in context: A032522 A077964 A077968 * A048572 A337561 A121173

Adjacent sequences: A123955 A123956 A123957 * A123959 A123960 A123961

Keyword

sign,easy

Author

Roger L. Bagula and Gary W. Adamson, Oct 27 2006

Status

approved