A274209 Decimal expansion of the reciprocal of the constant in A274192; see Comments.

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

Offset

0,1

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 0.67469726387...

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

Links

Table of n, a(n) for n=0..85.

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

Example

Limiting ratio = 0.6746972638734685572768086297549501...

Mathematica

z = 1600; 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]
d = RealDigits[u][[1]] (*A274209*)

Crossrefs

Cf. A274192, A274183, A274184, A274210, A274211.

Sequence in context: A098882 A254374 A019616 * A275276 A073177 A230848

Adjacent sequences: A274206 A274207 A274208 * A274210 A274211 A274212

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jun 16 2016

Status

approved