A296216 - OEIS

%I #4 Dec 09 2017 19:28:29

%S 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 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 3,1,5,4,1,7,9,3,7,0,4,5,8,4,1,2,6,2

%N Decimal expansion of the limiting ratio of terms in A296215.

%e A296215(n)/A296215(n-1)) -> 3.667759717...

%e See A296000 for a guide to related sequences and limiting ratios.

%t a[0] = 1; a[1] = 3; b[0] = 2;

%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}];  (* A296215 *)

%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]]    (* A296216 *)

%Y Cf. A296000, A296215, A296218.

%K nonn,easy,cons

%O 1,1

%A _Clark Kimberling_, Dec 08 2017