A097948 G.f.: -(1-3*x^2-x^3)/(1+4*x-4*x^3-x^4).

-1, 4, -13, 49, -181, 676, -2521, 9409, -35113, 131044, -489061, 1825201, -6811741, 25421764, -94875313, 354079489, -1321442641, 4931691076, -18405321661, 68689595569, -256353060613, 956722646884, -3570537526921, 13325427460801, -49731172316281, 185599261804324

Offset: 0

Author

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

Keywords

• sign
• easy

Comments

This is the sequence tesseq(X) with X = .5'i + .5i' + 'ii' - .5'jj' + 1.5'kk' - 1. See A108946.

Links

• Robert Munafo, Sequences Related to Floretions
• Index entries for linear recurrences with constant coefficients, signature (-4,0,4,1).

Crossrefs

Cf. A001353, A097947, A097949, A108946.

Programs

Mathematica

CoefficientList[Series[-(1-3x^2-x^3)/(1+4x-4x^3-x^4),{x,0,40}],x] (* or *) LinearRecurrence[{-4,0,4,1},{-1,4,-13,49},40] (* Harvey P. Dale, Sep 06 2014 *)

Formula

a(0)=-1, a(1)=4, a(2)=-13, a(3)=49, a(n)=-4*a(n-1)+4*a(n-3)+a(n-4). - Harvey P. Dale, Sep 06 2014

a(n) = (1 - (-1)^n + 2*cos(arccos(-2)*(n+1)))/4. - Eric Simon Jacob, Aug 17 2023

Extensions

Edited by Creighton Dement, Dec 11 2009