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A108171
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Tribonacci version of A076662 using beta positive real Pisot root of x^3-x^2-x-1.
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0
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4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Three part composition of sequence based on the Fibonacci subsitution twos order.
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FORMULA
| b(n)= 1+Ceiling[(n-1)*beta] a(n)=b(n)-b(n-1)
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MATHEMATICA
| NSolve[x^3 - x^2 - x - 1 = 0, x] beta = 1.8392867552141612 a[n_] = 1 + Ceiling[(n - 1)*beta^2] (* A007066 like*) aa = Table[a[n], {n, 1, 100}] (*A076662 like*) b = Table[a[n] - a[n - 1], {n, 2, Length[aa]}] F[1] = 2; F[n_] := F[n] = F[n - 1] + b[[n]] (* A000195 like*) c = Table[F[n], {n, 1, Length[b] - 1}]
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CROSSREFS
| Cf. A007066, A076662, A000195.
Sequence in context: A002285 A106049 A136627 * A106055 A171783 A168309
Adjacent sequences: A108168 A108169 A108170 * A108172 A108173 A108174
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 13 2005
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