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Number h such that (h,0) is n steps from (0,0), where steps are as follows: (x,y)->(x-r, y) if r > 0, and (x,y)->(y, r/3) otherwise, where r = x mod 3.
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%I #7 May 06 2015 09:48:24

%S 0,1,1,3,4,4,3,4,4,5,6,6,6,7,7,6,7,7,5,6,6,6,7,7,6,7,7,7,8,8,8,9,9,8,

%T 9,9,8,9,9,9,10,10,9,10,10,8,9,9,9,10,10,9,10,10,7,8,8,8,9,9,8,9,9,8,

%U 9,9,9,10,10,9,10,10,8,9,9,9,10,10,9,10,10

%N Number h such that (h,0) is n steps from (0,0), where steps are as follows: (x,y)->(x-r, y) if r > 0, and (x,y)->(y, r/3) otherwise, where r = x mod 3.

%C This is column 1 of the array at A253281.

%H Clark Kimberling, <a href="/A253718/b253718.txt">Table of n, a(n) for n = 0..1000</a>

%t f[{x_, y_}] := If[IntegerQ[x/3], {y, x/3}, {x - Mod[x, 3], y}];

%t g[{x_, y_}] := Drop[FixedPointList[f, {x, y}], -1];

%t Table[-1 + Length[g[{n, 0}]], {n, 0, 200}] (* A253718 *)

%Y Cf. A253281.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, May 02 2015