

A274192


Decimal expansion of limiting ratio described in Comments.


7



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
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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(n1,k1) + g(n1,2k) for n > 0, k > 1. The sum of numbers in the nth row of the array {g(n,k)} is given by A274184; viz., this sum is also the number of numbers in the nth 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(n1) and the numbers k/2 as k ranges through the even numbers k in h(n1), and then let H(n) be the number of numbers in h(n), then H(n)/H(n1) 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), 433443.


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 A197483
Adjacent sequences: A274189 A274190 A274191 * A274193 A274194 A274195


KEYWORD

nonn,cons,easy


AUTHOR

Clark Kimberling, Jun 13 2016


STATUS

approved



