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Search: id:A108175
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| A108175 |
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Three-step constructive order sequence. |
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+0
1
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| 3, 6, 11, 16, 20, 24, 28, 31, 36, 41, 46, 51, 56, 60, 65, 70, 75, 79, 84, 89, 94, 99, 103, 108, 113, 118, 122, 127, 132, 137, 142, 146, 149, 154, 158, 161, 165, 168, 172, 177, 180, 185, 190, 195, 199, 202, 206, 211, 216, 220, 224, 227, 230, 235, 238, 241, 246
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Average=4.32323
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FORMULA
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g[n]=switch between states[0, 1, 2] f[n]=5-Mod[g[n]-g[n-1], 3] a(n) = a[n-1]+f[n]
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EXAMPLE
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Modeled on construction of twos order sequence for Fibonacci substitution,
this construction of an order sequences produces a lower average than the
actual tribonacci ones order sequence.
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MATHEMATICA
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beta = x /. NSolve[x^3 - x^2 - x - 1 == 0, x][[3]]; a[1] = 0; a[2] = 4; a[n_] := a[n] = If[Mod[a[n - 1] - a[n - 2], 3] == 0, Ceiling[(n - 1)*beta^3] - 4, If[Mod[a[n - 1] - a[n - 2], 3] == 1, Ceiling[(n-1)*beta] - 1, Ceiling[(n - 1)*beta^2] - 2] ] aa = Table[a[n], {n, 1, 100}]; b = Table[5 - Mod[a[n] - a[n - 1], 3], {n, 2, Length[aa]}]; F[1] = 3; F[n_] := F[n] = F[n - 1] + b[[n]] c = Table[F[n], {n, 1, Length[b] - 1}]
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CROSSREFS
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Sequence in context: A131665 A132158 A099951 this_sequence A030722 A030720 A111582
Adjacent sequences: A108172 A108173 A108174 this_sequence A108176 A108177 A108178
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 13 2005
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