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A214999 Power floor sequence of sqrt(5).

%I A214999 #5 Nov 15 2012 21:24:39
%S A214999 2,4,8,17,38,84,187,418,934,2088,4668,10437,23337,52183,116684,260913,
%T A214999 583419,1304564,2917093,6522818,14585464,32614088,72927317,163070438,
%U A214999 364636584,815352188,1823182917,4076760937,9115914583
%N A214999 Power floor sequence of sqrt(5).
%C A214999 See A214992 for a discussion of power floor sequence and the power floor function, p1(x) = limit of a(n,x)/x^n.  The present sequence is a(n,r), where r = sqrt(5), and the limit p1(r) = 1.4935514451954997630823098687087959696356...
%H A214999 Clark Kimberling, <a href="/A214999/b214999.txt">Table of n, a(n) for n = 0..250</a>
%F A214999 a(n) = [x*a(n-1)], where x=sqrt(5), a(0) = [x].
%e A214999 a(0) = [r] = 2, where r = sqrt(5); a(1) = [2*r] = 4; a(2) = [4*r] = 8.
%t A214999 x = Sqrt[5]; z = 30; (* z = # terms in sequences *)
%t A214999 f[x_] := Floor[x]; c[x_] := Ceiling[x];
%t A214999 p1[0] = f[x]; p2[0] = f[x]; p3[0] = c[x]; p4[0] = c[x];
%t A214999 p1[n_] := f[x*p1[n - 1]]
%t A214999 p2[n_] := If[Mod[n, 2] == 1, c[x*p2[n - 1]], f[x*p2[n - 1]]]
%t A214999 p3[n_] := If[Mod[n, 2] == 1, f[x*p3[n - 1]], c[x*p3[n - 1]]]
%t A214999 p4[n_] := c[x*p4[n - 1]]
%t A214999 Table[p1[n], {n, 0, z}]  (* A214999 *)
%t A214999 Table[p2[n], {n, 0, z}]  (* A215091 *)
%t A214999 Table[p3[n], {n, 0, z}]  (* A218982 *)
%t A214999 Table[p4[n], {n, 0, z}]  (* A218983 *)
%Y A214999 Cf. A214992, A215091, A218982, A218983.
%K A214999 nonn,easy
%O A214999 0,1
%A A214999 _Clark Kimberling_, Nov 10 2012