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

Author

Creighton Dement, Apr 08 2009

Keywords

• easy
• sign

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).

Crossrefs

Cf. A159284, A159285, A159287, A159288.

Programs

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

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 *)

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

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