A274193 - OEIS

%I #5 Jun 16 2016 14:00:55

%S 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,2,2,2,1,1,1,1,3,3,2,2,1,

%T 1,1,1,3,4,3,2,2,1,1,1,1,4,4,4,3,2,2,1,1,1,1,5,6,5,4,3,2,2,1,1,1,1,6,

%U 7,7,5,4,3,2,2,1,1,1,1,8,9,8,7,5,4,3

%N Triangular array read by rows: g(n,k) = 1 for n >= 0; g(n,k) = 0 if k > n; g(n,k) = g(n-1,k-1) + g(n-1,3k) for n > 0, k > 1.

%H Clark Kimberling, <a href="/A274193/b274193.txt">Table of n, a(n) for n = 0..10000</a>

%e First  10 rows:

%e 1

%e 1   1

%e 1   1   1

%e 1   1   1   1

%e 1   2   1   1   1

%e 1   2   2   1   1   1

%e 1   2   2   2   1   1   1

%e 1   3   3   2   2   1   1   1

%e 1   3   4   3   2   2   1   1   1

%e 1   4   4   4   3   2   2   1   1   1

%t g[n_, 0] = g[n, 0] = 1;

%t g[n_, k_] := g[n, k] = If[k > n, 0, g[n - 1, k - 1] + g[n - 1, 3 k]];

%t t = Table[g[n, k], {n, 0, 14}, {k, 0, n}]

%t TableForm[t] (* A274193 array *)

%t u = Flatten[t] (* A274193 sequence *)

%Y Cf. A274194 (row sums), A274195, A274200 (limiting reverse row), A274190, A274196.

%K nonn,tabl,easy

%O 0,12

%A _Clark Kimberling_, Jun 14 2016