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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 (list; constant; graph; refs; listen; history; text; internal format)
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 A197483

Adjacent sequences:  A274189 A274190 A274191 * A274193 A274194 A274195

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Jun 13 2016

STATUS

approved

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Last modified August 10 11:12 EDT 2020. Contains 336379 sequences. (Running on oeis4.)