A097949 G.f.: -(2+7*x-x^3)/(1+4*x-4*x^3-x^4).

-2, 1, -4, 9, -34, 121, -452, 1681, -6274, 23409, -87364, 326041, -1216802, 4541161, -16947844, 63250209, -236052994, 880961761, -3287794052, 12270214441, -45793063714, 170902040409, -637815097924, 2380358351281, -8883618307202, 33154114877521, -123732841202884

Offset: 0

Author

N. J. A. Sloane, following a suggestion of Creighton Dement, Sep 06 2004

Keywords

• sign

Comments

This is the sequence "ves(n)".

Links

• Index entries for linear recurrences with constant coefficients, signature (-4,0,4,1).

Crossrefs

Cf. A001353, A097947, A097948.

Programs

Mathematica

CoefficientList[Series[-(2+7x-x^3)/(1+4x-4x^3-x^4),{x,0,40}],x] (* or *) LinearRecurrence[{-4,0,4,1},{-2,1,-4,9},40] (* Harvey P. Dale, Aug 11 2021 *)

Formula

a(n) = -(-1)^n - (1/6)*( ( -sqrt(3) - 2 )^n + ( sqrt(3) - 2 )^n ) - 2/3. - Eric Simon Jacob, Aug 18 2023