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A131040 a(n) = (1/2+1/2*i*sqrt(11))^n + (1/2-1/2*i*sqrt(11))^n, where i=sqrt(-1). 3

%I

%S 1,-5,-8,7,31,10,-83,-113,136,475,67,-1358,-1559,2515,7192,-353,

%T -21929,-20870,44917,107527,-27224,-349805,-268133,781282,1585681,

%U -758165,-5515208,-3240713,13304911,23027050,-16887683,-85968833,-35305784

%N a(n) = (1/2+1/2*i*sqrt(11))^n + (1/2-1/2*i*sqrt(11))^n, where i=sqrt(-1).

%C Generating floretion is 1.5i' + .5j' + .5k' + .5e whereas in A131039 it is 'i + .5i' + .5j' + .5k' + .5e

%C Essentially the Lucas sequence V(1,3). - _Peter Bala_, Jun 23 2015

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Lucas_sequence">Lucas sequence</a>

%F a(n) = a(n-1) - 3*a(n-2); G.f. (1 - 6*x)/(1 - x + 3*x^2).

%F a(n) = [x^n] ( (1 + x + sqrt(1 + 2*x - 11*x^2))/2 )^n. - _Peter Bala_, Jun 23 2015

%p Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[ 1.5i' + .5j' + .5k' + .5e]

%o (Sage) [lucas_number2(n,1,3) for n in range(1, 34)] # _Zerinvary Lajos_, May 14 2009

%Y Cf. A131039, A131041, A131042, A002316, A002531.

%K easy,sign

%O 0,2

%A _Creighton Dement_, Jun 11 2007

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Last modified April 13 16:36 EDT 2021. Contains 342936 sequences. (Running on oeis4.)