A274192 Decimal expansion of limiting ratio described in Comments.

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

Offset

1,2

Comments

As in A274190, 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-1,2k) for n > 0, k > 1. The sum of numbers in the n-th row of the array {g(n,k)} is given by A274184; viz., this sum is also the number of numbers in the n-th row of the array in A274183. In other words, if we put h(0) = (0) and for n > 0 define h(n) inductively as the concatenation of h(n-1) and the numbers k/2 as k ranges through the even numbers k in h(n-1), and then let H(n) be the number of numbers in h(n), then H(n)/H(n-1) approaches 1.48214622...

This constant appears on p. 439 of Tangora's paper cited in Links.

Links

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

M. C. Tangora, Level number sequences of trees and the lambda algebra, European J. Combinatorics 12 (1991), 433-443.

Example

Limiting ratio = 1.48214622104579647395109450508929...

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, 2 k]];
t = Table[g[n, k], {n, 0, z}, {k, 0, n}];
w = Map[Total, t];   (* A274184 *)
u = N[w[[z]]/w[[z - 1]], 100]
RealDigits[u][[1]] (* A274192 *)

Crossrefs

Cf. A274190, A274184, A274195, A274198, A274209 (reciprocal).

Sequence in context: A331331 A134484 A244641 * A021958 A200412 A368646

Adjacent sequences: A274189 A274190 A274191 * A274193 A274194 A274195

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jun 13 2016

Status

approved