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A296216
Decimal expansion of the limiting ratio of terms in A296215.
2
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
1,1
EXAMPLE
A296215(n)/A296215(n-1)) -> 3.667759717...
See A296000 for a guide to related sequences and limiting ratios.
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 *)
CROSSREFS
KEYWORD
nonn,easy,cons
AUTHOR
Clark Kimberling, Dec 08 2017
STATUS
approved