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

Author

Clark Kimberling, Jun 16 2016

Keywords

• nonn
• cons
• easy

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.

Examples

			Limiting ratio = 0.6746972638734685572768086297549501...
		

Links

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

Crossrefs

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

Programs

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*)