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A274195 Decimal expansion of limiting ratio described in Comments.

%I A274195 #5 Jun 16 2016 21:38:34
%S A274195 1,2,9,8,6,4,0,6,4,0,8,6,1,7,0,4,6,4,5,6,9,3,3,4,4,1,6,1,5,8,5,2,8,1,
%T A274195 2,2,0,4,8,5,5,3,9,7,7,9,8,6,5,3,7,4,5,6,3,3,1,4,5,5,4,9,3,9,2,7,3,5,
%U A274195 7,5,5,6,3,1,8,8,7,7,3,1,4,3,1,1,2,8
%N A274195 Decimal expansion of limiting ratio described in Comments.
%C A274195 As in A274193, define 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.  The sum of numbers in the n-th row of the array {g(n,k)} is given by A274194, and "limiting ratio" = limit of A274194(n)/A274194(n-1).
%e A274195 Limiting ratio = 1.2986406408617046456933441615...
%t A274195 z = 1500; g[n_, 0] = g[n, 0] = 1;
%t A274195 g[n_, k_] := g[n, k] = If[k > n, 0, g[n - 1, k - 1] + g[n - 1, 3 k]];
%t A274195 t = Table[g[n, k], {n, 0, z}, {k, 0, n}];
%t A274195 w = Map[Total, t];   (* A274194 *)
%t A274195 u = N[w[[z]]/w[[z - 1]], 100]
%t A274195 RealDigits[u][[1]] (* A274195 *)
%Y A274195 Cf. A274193, A274194, A274198, A274210 (reciprocal).
%K A274195 nonn,cons,easy
%O A274195 1,2
%A A274195 _Clark Kimberling_, Jun 16 2016