A274198 Decimal expansion of limiting ratio described in Comments.

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

Offset

1,2

Comments

As in A274193, define g(n,k) = 1 for n >= 0; g(n,k) = 0 if k > n; g(n,k) = g(n-1,k-1) + g(n-1,4k) for n > 0, k > 1. The sum of numbers in the n-th row of the array {g(n,k)} is given by A274197, and "limiting ratio" = limit of A274197(n)/A274197(n-1).

Links

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

Example

limiting ratio = 1.21297992704936771891526402555...

Mathematica

z = 1500; g[n_, 0] = g[n, 0] = 1;
g[n_, k_] := g[n, k] = If[k > n, 0, g[n - 1, k - 1] + g[n - 1, 4 k]];
t = Table[g[n, k], {n, 0, z}, {k, 0, n}];
w = Map[Total, t];   (* A274197 *)
u = N[w[[z]]/w[[z - 1]], 100]
RealDigits[u][[1]] (* A274198 *)

Crossrefs

Cf. A274196, A274197, A274192, A274193, A274211 (reciprocal).

Sequence in context: A022694 A173159 A271574 * A002079 A006126 A078357

Adjacent sequences: A274195 A274196 A274197 * A274199 A274200 A274201

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jun 16 2016

Status

approved