A296222 Decimal expansion of the limiting ratio of terms in A296221.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..86.

Example

A296221(n)/A296221(n-1)) -> 3.651119422238034...

Mathematica

mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];
a[0] = 1; a[1] = 3; b[0] = 2;
a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 0, n - 1}] + 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}];  (* A296221 *)
Table[b[n], {n, 0, 20}]
N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
RealDigits[Last[t], 10][[1]] (* A296222 *)

Crossrefs

Cf. A296000, A296215, A296217.

Sequence in context: A224746 A367036 A296226 * A295999 A296224 A135097

Adjacent sequences: A296219 A296220 A296221 * A296223 A296224 A296225

Keyword

nonn,easy,cons

Author

Clark Kimberling, Dec 09 2017

Status

approved