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

1,3

Comments

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

Links

Table of n, a(n) for n=1..38.

Formula

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

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]}]

Crossrefs

Cf. A000931.

Sequence in context: A316154 A079741 A000861 * A245905 A366482 A087146

Adjacent sequences: A108165 A108166 A108167 * A108169 A108170 A108171

Keyword

nonn,uned

Author

Roger L. Bagula, Jun 13 2005

Status

approved