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A274198 Decimal expansion of limiting ratio described in Comments.

%I A274198 #5 Jun 16 2016 21:42:50
%S A274198 1,2,1,2,9,7,9,9,2,7,0,4,9,3,6,7,7,1,8,9,1,5,2,6,4,0,2,5,5,5,1,1,2,8,
%T A274198 7,8,2,2,9,0,2,7,9,5,6,9,9,8,9,8,8,9,8,2,0,7,0,0,8,7,4,0,8,0,6,8,2,8,
%U A274198 0,2,4,2,2,2,4,4,4,3,7,3,5,3,1,3,4,9
%N A274198 Decimal expansion of limiting ratio described in Comments.
%C A274198 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-1,4k) for n > 0, k > 1.  The sum of numbers in the n-th row of the array {g(n,k)} is given by A274197, and "limiting ratio" = limit of A274197(n)/A274197(n-1).
%e A274198 limiting ratio = 1.21297992704936771891526402555...
%t A274198 z = 1500; g[n_, 0] = g[n, 0] = 1;
%t A274198 g[n_, k_] := g[n, k] = If[k > n, 0, g[n - 1, k - 1] + g[n - 1, 4 k]];
%t A274198 t = Table[g[n, k], {n, 0, z}, {k, 0, n}];
%t A274198 w = Map[Total, t];   (* A274197 *)
%t A274198 u = N[w[[z]]/w[[z - 1]], 100]
%t A274198 RealDigits[u][[1]] (* A274198 *)
%Y A274198 Cf. A274196, A274197, A274192, A274193, A274211 (reciprocal).
%K A274198 nonn,cons,easy
%O A274198 1,2
%A A274198 _Clark Kimberling_, Jun 16 2016