A105225 - OEIS

%I #20 Sep 01 2024 20:02:05

%S 1,-1,-2,1,6,5,-6,-15,-2,29,34,-23,-90,-43,138,225,-50,-499,-398,601,

%T 1398,197,-2598,-2991,2206,8189,3778,-12599,-20154,5045,45354,35265,

%U -55442,-125971,-15086,236857,267030,-206683,-740742,-327375,1154110,1808861,-499358,-4117079,-3118362,5115797

%N a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = -1, a(2) = -2.

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

%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_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, -3, 2).

%F a(n) - a(n+1) = A002249(n).

%F a(n) = (A002249(n+1) + 1)/2.

%F From _Harvey P. Dale_, Jul 23 2012: (Start)

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

%F a(n)=1/2*(1+(1/2*(1-I*Sqrt[7]))^n+(1/2*(1+I*Sqrt[7]))^n). (End)

%t LinearRecurrence[{2,-3,2},{1,-1,-2},50] (* or *) CoefficientList[ Series[ (-3*x^2+3*x-1)/(2*x^3-3*x^2+2*x-1),{x,0,50}],x] (* _Harvey P. Dale_, Jul 23 2012 *)

%Y Cf. A002249, A014551.

%K sign,easy

%O 0,3

%A _Creighton Dement_, Apr 14 2005