A007150 - OEIS

A007150

2-part of number of tournaments on n nodes.
(Formerly M0269)

0, 0, 1, 2, 2, 3, 3, 5, 4, 6, 5, 7, 6, 7, 7, 10, 8, 9, 9, 12, 10, 11, 11, 14, 12, 14, 13, 15, 14, 17, 15, 19, 16, 20, 17, 19, 18, 19, 19, 26, 20, 22, 21, 23, 22, 23, 23, 30, 24, 26, 25, 28, 26, 27, 27, 30, 28, 30, 29, 33, 30, 31, 31, 35, 32, 34, 33, 38, 34, 37, 35, 38, 36, 38, 37, 39

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

OFFSET

1,4

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..141

Steven C. Cater and Robert W. Robinson, Exponents of 2 in the numbers of unlabeled graphs and tournaments, Congressus Numerantium, 82 (1991), pp. 139-155.

Steven C. Cater and Robert W. Robinson, Exponents of 2 in the numbers of unlabeled graphs and tournaments, Preprint. (Annotated scanned copy)

Index entries for sequences related to tournaments

FORMULA

a(n) = A007814(A000568(n)). - Michel Marcus, Jan 06 2020

MATHEMATICA

A000568 = Cases[Import["https://oeis.org/A000568/b000568.txt", "Table"], {_, _}][[All, 2]];

IntegerExponent[#, 2]& /@ A000568 // Rest (* Jean-François Alcover, Jan 06 2020 *)

PROG

(Python)

from itertools import product

from math import prod, factorial, gcd

from fractions import Fraction

from sympy.utilities.iterables import partitions

def A007150(n): return (~(m:=int(sum(Fraction(1<<(sum(p[r]*p[s]*gcd(r, s) for r, s in product(p.keys(), repeat=2))-sum(p.values())>>1), prod(q**p[q]*factorial(p[q]) for q in p)) for p in partitions(n) if all(q&1 for q in p)))) & m-1).bit_length() # Chai Wah Wu, Jul 01 2024

CROSSREFS

Power of 2 dividing A000568(n). Cf. A007814.

Sequence in context: A342515 A307815 A070230 * A213634 A300271 A252461

Adjacent sequences: A007147 A007148 A007149 * A007151 A007152 A007153

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from A000568 by Jean-François Alcover, Jan 06 2020

STATUS

approved