A097948 - OEIS

%I #20 Sep 16 2023 17:56:52

%S -1,4,-13,49,-181,676,-2521,9409,-35113,131044,-489061,1825201,

%T -6811741,25421764,-94875313,354079489,-1321442641,4931691076,

%U -18405321661,68689595569,-256353060613,956722646884,-3570537526921,13325427460801,-49731172316281,185599261804324

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

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

%H Robert Munafo, <a href="http://www.mrob.com/pub/math/seq-floretion.html">Sequences Related to Floretions</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-4,0,4,1).

%F 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

%F a(n) = (1 - (-1)^n + 2*cos(arccos(-2)*(n+1)))/4. - _Eric Simon Jacob_, Aug 17 2023

%t 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 *)

%Y Cf. A001353, A097947, A097949, A108946.

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_, following a suggestion of _Creighton Dement_, Sep 06 2004

%E Edited by _Creighton Dement_, Dec 11 2009