%I #32 Mar 17 2024 12:55:46

%S 1,-1,2,-1,0,2,-3,3,-1,-2,5,-6,4,1,-7,11,-10,3,8,-18,21,-13,-5,26,-39,

%T 34,-8,-31,65,-73,42,23,-96,138,-115,19,119,-234,253,-134,-100,353,

%U -487,387,-34,-453,840,-874,421,419,-1293,1714,-1295,2,1712,-3007,3009,-1297,-1710,4719,-6016

%N Expansion of g.f. (1+x^2)/(1+x-x^3).

%C A floretion-generated sequence.

%C Floretion Algebra Multiplication Program, FAMP Code: Define A = + .5'i + .5'j + .5'k + .5e and B = + .5'i + .5i' + .5'ii' + .5e. Then (a(n)) = jesloop(infty)-jesleftfor[A*B], ForType: 1A.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1).

%F Recurrence: a(n+3) = a(n) - a(n+2); a(0) = 1, a(1) = -1, a(2) = 2.

%F a(n+1) - a(n) = ((-1)^(n+1))*a(n+5); a(n) = A104771(n) - A104769(n).

%F a(n+1) = -(A104769(n) + A104769(n+2)), n>=0. - _Ralf Stephan_, Apr 05 2009

%t CoefficientList[Series[(1+x^2)/(1+x-x^3),{x,0,60}],x] (* or *) LinearRecurrence[ {-1,0,1},{1,-1,2},70] (* _Harvey P. Dale_, Jan 27 2013 *)

%Y Cf. A104769, A104771.

%K sign,easy

%O 0,3

%A _Creighton Dement_, Mar 24 2005

%E Edited by _Ralf Stephan_, Apr 05 2009