%I #5 Mar 31 2012 20:47:12
%S 0,1,2,3,5,9,12,21,37,65,114,200,265,465,816,1432,2513,4410,5842,
%T 10252,17991,31572,55405,97229,128801,226030,396655,696081,1221537,
%U 2143648,3761840,4983377,8745217,15346786,26931732,47261895,82938844,109870576
%N Padovan sequence for indices of the Beatty sequence of the tribonacci constant.
%C Limit[a(n)/a(n-1),n->Infinity]={1.32472, 1.75488, 1.75488, 1.75488, 1.75488, 1.75488}
%F a(n) = A000931(3+(A158919(n)). - R. J. Mathar, Sep 11 2011
%t 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]}]
%Y Cf. A000931.
%K nonn,uned
%O 1,3
%A _Roger L. Bagula_, Jun 13 2005
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