|
%I #3 Mar 31 2012 20:47:12
%S 1,1,1,3,18,33,111,690,1269,4292,26705,49118,166165,1033922,1901679,
%T 6433333,40029886,73626439,249076459,1549819116,2850561773,9643381402,
%U 60003650693,110363919984,373358466957,2323134396636,4272910326315
%N Alternating three ratio switched sequence based on characteristic root of A000931.
%C Limit[a(n)/a(n-1),n->Infinity]={1.83929, 3.38298, 6.22226}
%F if Mod[n, 3]=0 then F[n] = Floor[beta*F[n-1]] if Mod[n, 3]=1 then F[n] = Floor[beta^2*F[n-1]] if Mod[n, 3]=2 then F[n] = Floor[beta^3*F[n-1]] a(n) = F[n]
%t NSolve[x^3 - x^2 - x - 1 == 0, x] beta = 1.8392867552141612; F[1] = 1; F[2] = 1; F[n__] := F[n] = If[Mod[n, 3] == 0, Floor[beta*F[n - 1]], If[ Mod[n, 3] == 1, Floor[(beta^2)*F[n - 1]], Floor[(beta^3)*F[n - 1]]]] a = Table[F[n], {n, 1, 50}] an = Table[N[a[[n]]/a[[n - 1]]], {n, 6, 50}]
%Y Cf. A000931.
%K nonn,uned
%O 0,4
%A _Roger L. Bagula_, Jun 13 2005
|
