%I #7 Mar 30 2012 17:34:13
%S 0,0,2,-2,-1,0,0,0,1,-1,-1,0,0,0,1,-1,-1,0,0,0,1,-1,-1,0,0,0,1,-1,-1,
%T 0,0,0,1,-1,-1,0,0,0,1,-1,-1,0,0,0,1,-1,0,1,0,0,2,-2,-1,0,0,0,1,-2,-1,
%U 0,0,0,1,-1,0,1,3,-2,1,0,0,1,3,-2,1,0,0,1,3,-2,1,0,0,1,3,-2,1,0,0,1,3,-2,1,0,0,1,3,-2,1,0,0,1,3,-2,1,0,0,1,3,-2,1,0,0,1,3
%N Let m0 be the matrix {{0,1,0},{0,1,1},{1,0,-q}}, m1={{0,1,0},{0,0,1},{1,1,q1}}; if n even a(n) = (3,3)-element of m[n-1]*m0, if n odd a(n) = (3,3)-element of m[n-1]*m1.
%C Alternating even-odd matrix recursive sequence using the x^3-x^2-x-1=0 Pisot balanced by the x^3-x-1=0 minimal Pisot.
%C A new minimal Pisot recursive matrix developed with eigenvalue equation x^3-x-1=0 using the Blackmore-Kappraff "bonacci" matrix as the pattern.
%t (* Adamson's matrix functions alternating x^3 Pisot and minimal Pisot*) digits=200 Solve[x^3-x-1==0, x] k=positive root of minimal Pisot q=N[k^2-1/k, 20] m0={{0, 1, 0}, {0, 1, 1}, {1, 0, -q}} NSolve[x^3-x^2-x-1==0, x] k1=1.83928675521416113 q1=k1^2-k1-1/k1 m1={{0, 1, 0}, {0, 0, 1}, {1, 1, q1}} m[n_Integer?Positive] := If[Mod[n, 2]==0, m[n-1].m0, m[n-1].m1] m[0] = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}} a=Table[Floor[m[n][[3, 3]]], {n, 1, digits}]
%K sign
%O 1,3
%A _Roger L. Bagula_, Dec 03 2003