%I #12 Jun 13 2015 00:52:36

%S 0,1,3,8,20,47,105,224,456,881,1595,2632,3692,3359,-2927,-27776,

%T -103088,-304607,-803149,-1966392,-4549884,-10029361,-21114759,

%U -42375200,-80491880,-142437359,-226667157,-294543992,-191015460,556551487,3216934945

%N Imaginary parts of terms (1,1), (2,2) of matrix [1,(1+I); 1,1]^n.

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

%F Imaginary parts of upper left and lower right terms of matrix [1,(1+I); 1,1]^n; I^2 = -1.

%F a(n) = 4*a(n-1)-4*a(n-2)-a(n-4). G.f.: -x^2*(x-1) / (x^4+4*x^2-4*x+1). [_Colin Barker_, Dec 18 2012]

%e a(6) = 47 since the sixth power of the matrix generator = [(14,47); (-6,58); (26,32); (14,47)]; where (14,47) = (14 + 47*I).

%K sign,easy

%O 1,3

%A _Gary W. Adamson_, Mar 30 2008