A108175 Three-step constructive order sequence.

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

Offset

0,1

Comments

Average=4.32323

Links

Table of n, a(n) for n=0..56.

Formula

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]

Example

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.

Mathematica

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}]

Crossrefs

Sequence in context: A190455 A310107 A099951 * A030722 A030720 A310108

Adjacent sequences: A108172 A108173 A108174 * A108176 A108177 A108178

Keyword

nonn,uned

Author

Roger L. Bagula, Jun 13 2005

Status

approved