A072404 Denominator of the Reingold-Tarjan sequence, numerator=A072403.

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

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