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A108171 Tribonacci version of A076662 using beta positive real Pisot root of x^3 - x^2 - x - 1. 0

%I #12 Jun 14 2019 00:30:06

%S 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,

%T 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,

%U 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

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

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

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

%t 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}]

%Y Cf. A007066, A076662, A000195.

%K nonn,uned

%O 0,1

%A _Roger L. Bagula_, Jun 13 2005

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)