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A296216 Decimal expansion of the limiting ratio of terms in A296215.

%I A296216 #7 Mar 15 2025 02:57:47
%S A296216 3,6,6,7,7,5,9,7,1,7,2,4,6,5,8,5,5,2,4,6,7,0,1,8,7,1,3,2,7,2,4,2,0,8,
%T A296216 5,4,4,0,7,4,0,1,0,7,4,6,0,9,5,0,2,0,6,5,5,6,3,7,5,6,4,7,4,5,6,7,3,8,
%U A296216 3,1,5,4,1,7,9,3,7,0,4,5,8,4,1,2,6,2
%N A296216 Decimal expansion of the limiting ratio of terms in A296215.
%e A296216 A296215(n)/A296215(n-1) -> 3.667759717...
%e A296216 See A296000 for a guide to related sequences and limiting ratios.
%t A296216 a[0] = 1; a[1] = 3; b[0] = 2;
%t A296216 a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 1, n - 1}];
%t A296216 b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
%t A296216 u = Table[a[n], {n, 0, 200}];  (* A296215 *)
%t A296216 Table[b[n], {n, 0, 20}]
%t A296216 N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
%t A296216 RealDigits[Last[t], 10][[1]]    (* A296216 *)
%Y A296216 Cf. A296000, A296215, A296218.
%K A296216 nonn,easy,cons
%O A296216 1,1
%A A296216 _Clark Kimberling_, Dec 08 2017