A108169 Alternating three ratio switched sequence based on characteristic root of A000931.

1, 1, 1, 3, 18, 33, 111, 690, 1269, 4292, 26705, 49118, 166165, 1033922, 1901679, 6433333, 40029886, 73626439, 249076459, 1549819116, 2850561773, 9643381402, 60003650693, 110363919984, 373358466957, 2323134396636, 4272910326315

Offset: 0

Author

Roger L. Bagula, Jun 13 2005

Keywords

• nonn
• uned

Comments

Limit[a(n)/a(n-1),n->Infinity]={1.83929, 3.38298, 6.22226}

Crossrefs

Cf. A000931.

Programs

Mathematica

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}]

Formula

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]