A108171 Tribonacci version of A076662 using beta positive real Pisot root of x^3 - x^2 - x - 1.

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

Offset: 0

Author

Roger L. Bagula, Jun 13 2005

Keywords

• nonn
• uned

Comments

Three part composition of sequence based on the Fibonacci substitution twos order.

Crossrefs

Cf. A007066, A076662, A000195.

Programs

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}]

Formula

b(n) = 1 + ceiling((n-1)*beta); a(n) = b(n) - b(n-1).