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A108169
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Alternating three ratio switched sequence based on characteristic root of A000931.
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0
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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
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OFFSET
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0,4
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COMMENTS
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Limit[a(n)/a(n-1),n->Infinity]={1.83929, 3.38298, 6.22226}
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LINKS
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FORMULA
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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]
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn,uned
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AUTHOR
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STATUS
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approved
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