login
A274209
Decimal expansion of the reciprocal of the constant in A274192; see Comments.
4
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
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
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Jun 16 2016
STATUS
approved