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A072404 Denominator of the Reingold-Tarjan sequence, numerator=A072403. 2
1, 3, 9, 9, 27, 27, 3, 27, 81, 81, 27, 81, 81, 9, 81, 81, 243, 243, 27, 243, 243, 81, 243, 243, 81, 243, 243, 27, 243, 243, 81, 243, 729, 729, 243, 729, 729, 81, 729, 729, 243, 729, 729, 243, 729, 729, 9, 729, 729, 243, 729, 729, 243, 729, 729, 81 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Reingold-Tarjan sequence is based on the following function defined on even positive integers and range of the rational numbers:

f(2*n) = if n is even then 2*f(n)/3 else (f(n+1)+f(n-1))/3 for n>1, f(2*1)=1.

f(2*n) = A072403(n)/a(n) for n>1, A072403(1)=1 and a(1)=1.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197; preprint. See Example 33.

E. M. Reingold and R. E. Tarjan, On a greedy heuristic for complete matching, SIAM J. Computing 10 (1981), 676-681; Semantic Scholar.

FORMULA

A072403(n) / a(n) = 1 - Sum_{k=1..n} (1 / A000244(A029837(k)). - Reinhard Zumkeller, Jan 01 2013

PROG

(Haskell)

import Data.Ratio ((%), denominator)

a072404 n = a072404_list !! (n-1)

a072404_list = map denominator $

               scanl1 (-) $ map ((1 %) . a000244) $ a029837_list

-- Reinhard Zumkeller, Jan 01 2013

CROSSREFS

Cf. A000244, A029837, A072403 (numerators).

Sequence in context: A206700 A162349 A223022 * A222996 A268026 A268019

Adjacent sequences:  A072401 A072402 A072403 * A072405 A072406 A072407

KEYWORD

nonn,frac

AUTHOR

Reinhard Zumkeller, Jun 16 2002

STATUS

approved

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Last modified August 5 07:21 EDT 2020. Contains 336209 sequences. (Running on oeis4.)