Tomas Boothby - cp's OEIS frontend

User: Tomas Boothby

Tomas Boothby has authored 2 sequences.

A232545 Number of Euler tours of the complete digraph on n vertices.

1, 3, 256, 972000, 247669456896, 6022251970560000000, 18932148110851728998400000000, 10036271333655026636037644353536000000000, 1135547314049215265041779022180122624000000000000000000, 33878761698754076709292639330840075944838638855101181276979200000000000

Offset: 2

Tomas Boothby, Nov 25 2013

			For n = 2, there is one Euler tour, (1,2,1), since (1,2,1) is cyclically equivalent to (2,1,2).
For n = 3, there are three Euler tours: (1,2,1,3,2,3,1), (1,2,3,1,3,2,1), (1,2,3,2,1,3,1).

Andrew Howroyd, Table of n, a(n) for n = 2..30
Wikipedia, BEST Theorem, a formula for counting Euler tours in digraphs.

a(n) = n^(n-2)*(n-2)!^n \\ Andrew Howroyd, Dec 28 2021

a(n) = n^(n-2)*(n-2)!^n, by the "BEST Theorem". - James Thompson, Jul 18 2017, Günter Rote, Dec 09 2021

The above formula can be written as a(n) = A000272(n)*A000142(n-2)^n. - Omar E. Pol, Jul 18 2017

a(5) corrected by Tomas Boothby, Dec 03 2013

Terms a(8) and beyond from Andrew Howroyd, Dec 28 2021

A127834 Numbers whose 8-bit binary representation, when rotated by up to one bit, contains every 3-bit binary representation for the numbers 0 through 7.

Original entry on oeis.org

23, 29, 46, 58, 71, 92, 113, 116, 139, 142, 163, 184, 197, 209, 226, 232

Offset: 1

Tomas Boothby, Feb 01 2007

The binary representations of these numbers are equivalent under rotation / complement.

When this binary representation, with two bits from one end concatenated to the other, is given as input to an elementary cellular automaton, the first line of output will uniquely identify the rule of the automaton.

			23 has the 8-bit representation 00010111.
Concatenate the last two digits onto the beginning to get 1100010111.
We read off the 3-bit substrings:
110
100
000
001
010
101
011
111

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

i = 0
while i < 256:
    bin = i.binary()
    bin = bin[ -2:] + "0"*(8-len(bin)) + bin
    subs = []
    for j in range(8):
        k = bin[j:j+3]
        if k not in subs:
            subs.append(k)
        else: break
    if len(subs) == 8: print(i)
    i += 1

cp's OEIS Frontend

User: Tomas Boothby

A232545 Number of Euler tours of the complete digraph on n vertices.

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