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

0,2

Comments

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

Links

Table of n, a(n) for n=0..25.

Robert Munafo, Sequences Related to Floretions

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

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

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 *)

Crossrefs

Cf. A001353, A097947, A097949, A108946.

Sequence in context: A300579 A180007 A338862 * A096971 A149451 A149452

Adjacent sequences: A097945 A097946 A097947 * A097949 A097950 A097951

Keyword

sign,easy

Author

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

Extensions

Edited by Creighton Dement, Dec 11 2009

Status

approved