A108168 Padovan sequence for indices of the Beatty sequence of the tribonacci constant.

0, 1, 2, 3, 5, 9, 12, 21, 37, 65, 114, 200, 265, 465, 816, 1432, 2513, 4410, 5842, 10252, 17991, 31572, 55405, 97229, 128801, 226030, 396655, 696081, 1221537, 2143648, 3761840, 4983377, 8745217, 15346786, 26931732, 47261895, 82938844, 109870576

Offset: 1

Author

Roger L. Bagula, Jun 13 2005

Keywords

• nonn
• uned

Comments

Limit[a(n)/a(n-1),n->Infinity]={1.32472, 1.75488, 1.75488, 1.75488, 1.75488, 1.75488}

Crossrefs

Cf. A000931.

Programs

Mathematica

NSolve[x^3 - x^2 - x - 1 = 0, x] beta = 1.8392867552141612 F[1] = 0; F[2] = 1; F[3] = 1; F[n__] := F[n] = F[n - 2] + F[n - 3] a1 = Table[F[Floor[beta*n]], {n, 1, 50}] Table[N[a1[[n]]/a1[[n - 1]]], {n, 3, Length[a1]}]

Formula

a(n) = A000931(3+A158919(n)). - R. J. Mathar, Sep 11 2011