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

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

Offset: 1

Author

Clark Kimberling, Dec 08 2017

Keywords

• nonn
• easy
• cons

Examples

			A296215(n)/A296215(n-1) -> 3.667759717...
See A296000 for a guide to related sequences and limiting ratios.
		

Crossrefs

Cf. A296000, A296215, A296218.

Programs

Mathematica

a[0] = 1; a[1] = 3; b[0] = 2;
a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 1, n - 1}];
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
u = Table[a[n], {n, 0, 200}];  (* A296215 *)
Table[b[n], {n, 0, 20}]
N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
RealDigits[Last[t], 10][[1]]    (* A296216 *)