A296224 Decimal expansion of the limiting ratio of terms in A296223.

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

Offset

1,1

Comments

A296223(n)/A296223(n-1)) -> 3.651440004884...

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

Links

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

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}]]];
Table[a[n], {n, 0, 200}]  (* A296223 *)
Table[b[n], {n, 0, 20}]
N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
RealDigits[Last[t], 10][[1]] (* A296224 *)

Crossrefs

Cf. A296000, A296223.

Sequence in context: A296226 A296222 A295999 * A135097 A154008 A144179

Adjacent sequences: A296221 A296222 A296223 * A296225 A296226 A296227

Keyword

nonn,easy,cons

Author

Clark Kimberling, Dec 10 2017

Status

approved