A274185 - OEIS

%I #9 Jun 21 2016 11:03:30

%S 0,1,2,0,3,1,4,2,1,0,5,3,2,1,0,6,4,3,2,1,2,1,0,7,5,4,3,2,3,2,1,1,0,0,

%T 8,6,5,4,3,4,3,2,2,1,1,3,2,1,1,0,0,9,7,6,5,4,5,4,3,3,2,2,4,3,2,2,1,1,

%U 2,1,1,0,0,1,0,0,10,8,7,6,5,6,5,4,4,3

%N Irregular triangular array having n-th row g(n) defined in Comments.

%C Let g(0) = (0) and for n > 0, define g(n) inductively to be the concatenation of g(n-1) and the numbers (k-1)/2 as k ranges through the odd numbers k in g(n-1).  Every nonnegative integer appears infinitely many times.  For the limiting ratio of lengths of consecutive rows, see A274192.

%e First seven rows:

%e 0

%e 1

%e 2   0

%e 3   1

%e 4   2   1   0

%e 5   3   2   1   0

%e 6   4   3   2   1   2   1   0

%t g[0] = {0}; z = 14; g[n_] := g[n] = Join[g[n - 1] + 1, (1/2) (Select[g[n - 1], IntegerQ[(# - 1)/2] &] - 1)]; Flatten[Table[g[n], {n, 0, z}]]

%Y Cf. A274142 (row lengths), A274192, A274183.

%K nonn,tabf,easy,base

%O 0,3

%A _Clark Kimberling_, Jun 13 2016