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A115315
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L = (1 + Sqrt[5])/(2*Sqrt[5]) Phi = (1 + Sqrt[5])/2 a(n) = Floor[L^3*{Phi^(3*n - 2), Phi^(3*n - 1), Phi^(3*n - 2) + Phi^(3*n - 1)}].
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0
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0, 0, 1, 2, 4, 6, 11, 17, 28, 46, 75, 121, 197, 319, 516, 836, 1353, 2189, 3542, 5731, 9273, 15004, 24278, 39283, 63562, 102845, 166408, 269253, 435661, 704915, 1140577, 1845492, 2986070, 4831563, 7817633, 12649197, 20466831, 33116028
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| N[Table[a[[n + 1]]/a[[n]], {n, 3, Length[a] - 1}]]-->Phi So it is Fibonacci like, too. Here how it goes: Form the matrix: M={{f[n],f[n+2},{f[n+1],f[n+3]} f3[n_]out=Det[M]*{f[[n],f[n+1],f[n+2}} All I did was use the L function equivalents in each position to derive the new sequence.
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MATHEMATICA
| L = (1 + Sqrt[5])/(2*Sqrt[5]) Phi = (1 + Sqrt[5])/2 f[n_] = Floor[L^3*{Phi^(3*n - 2), Phi^(3*n - 1), Phi^(3*n - 2) + Phi^(3*n - 1)}] a = Flatten[Table[f[n], {n, 1, 25}]]
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CROSSREFS
| Cf. A000045.
Sequence in context: A056342 A094719 A018144 * A004698 A014217 A034297
Adjacent sequences: A115312 A115313 A115314 * A115316 A115317 A115318
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 06 2006
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