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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-1,2k) for n > 0, k > 1.
6

%I #6 Jun 16 2016 13:59:12

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

%T 1,1,1,7,8,7,5,3,2,1,1,1,9,12,10,8,5,3,2,1,1,1,13,17,15,11,8,5,3,2,1,

%U 1,1,18,24,22,17,12,8,5,3,2,1,1,1,25,35,32

%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-1,2k) for n > 0, k > 1.

%H Clark Kimberling, <a href="/A274190/b274190.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 2 1 1

%e 1 2 2 1 1

%e 1 3 3 2 1 1

%e 1 4 4 3 2 1 1

%e 1 5 6 5 3 2 1 1

%e 1 7 8 7 5 3 2 1 1

%e 1 9 12 10 8 5 3 2 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, 2 k]];

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

%t TableForm[t] (* A274190 array *)

%t u = Flatten[t] (* A274190 sequence *)

%Y Cf. A274184 (row sums), A274192, A274199 (limiting reverse row), A274193, A274196.

%K nonn,tabl,easy

%O 0,8

%A _Clark Kimberling_, Jun 13 2016