A159286 Expansion of (x-1)^2/(1-x^2-2*x^3).

1, -2, 2, 0, -2, 4, -2, 0, 6, -4, 6, 8, -2, 20, 14, 16, 54, 44, 86, 152, 174, 324, 478, 672, 1126, 1628, 2470, 3880, 5726, 8820, 13486, 20272, 31126, 47244, 71670, 109496, 166158, 252836, 385150, 585152

Offset

0,2

Comments

A floretion-generated sequence: 'i + 0.5('ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj').

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Creighton Dement, Online Floretion Multiplier [broken link].

Index entries for linear recurrences with constant coefficients, signature (0,1,2).

Formula

a(n) = A159288(n) - 3*A159287(n+1). - R. J. Mathar, Apr 10 2009

a(1)=1, a(2)=-2, a(3)=2, a(n) = 1*a(n-2) + 2*a(n-3) for n >= 3. - Harvey P. Dale, Apr 24 2011

a(n) = A078026(n)-A078026(n-1). - R. J. Mathar, Mar 23 2023

Mathematica

CoefficientList[Series[(x-1)^2/(1-x^2-2*x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 1, 2}, {1, -2, 2}, 40]  (* Harvey P. Dale, Apr 24 2011 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 2, 1, 0]^n*[1; -2; 2])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016
(Magma) I:=[1, -2, 2]; [n le 3 select I[n] else Self(n-2) + 2*Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 27 2018

Crossrefs

Cf. A159284, A159285, A159287, A159288.

Sequence in context: A074823 A226177 A159916 * A355837 A261277 A006462

Adjacent sequences: A159283 A159284 A159285 * A159287 A159288 A159289

Keyword

easy,sign

Author

Creighton Dement, Apr 08 2009

Status

approved