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%I #4 Dec 09 2017 19:28:43
%S 4,3,1,4,1,8,6,9,6,3,4,0,2,6,0,0,1,2,6,3,9,6,2,5,4,6,9,6,2,5,5,3,9,9,
%T 3,1,3,1,7,3,1,5,4,3,3,5,3,7,7,6,9,7,3,4,5,0,0,3,0,4,5,3,5,4,9,2,4,3,
%U 5,8,4,1,6,4,5,9,6,9,2,4,1,0,0,4,3,4
%N Decimal expansion of the limiting ratio of terms in A296217.
%e A296217(n)/A296217(n-1)) -> 4.31418696340...
%e See A296000 for a guide to related sequences and limiting ratios.
%t a[0] = 1; a[1] = 2; b[0] = 3;
%t a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 1, n - 1}];
%t b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
%t u = Table[a[n], {n, 0, 200}]; (* A296217 *)
%t Table[b[n], {n, 0, 20}]
%t N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
%t RealDigits[Last[t], 10][[1]] (* A296218 *)
%Y Cf. A296000, A296215, A296217.
%K nonn,easy,cons
%O 1,1
%A _Clark Kimberling_, Dec 08 2017
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