A296228 Decimal expansion of the limiting ratio of terms in A296227.

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

Offset

1,1

Comments

A296227(n)/A296227(n-1)) -> 4.3033963031...

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] = 2; b[0] = 3;
a[n_] := a[n] = - n + Sum[a[k]*b[n - k - 1], {k, 0, n - 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}]  (* A296227 *)
Table[b[n], {n, 0, 20}]
N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
RealDigits[Last[t], 10][[1]] (* A296228 *)

Crossrefs

Cf. A296000, A296227.

Sequence in context: A227423 A199443 A142723 * A267410 A016697 A086466

Adjacent sequences: A296225 A296226 A296227 * A296229 A296230 A296231

Keyword

nonn,easy,cons

Author

Clark Kimberling, Dec 10 2017

Status

approved