cp's OEIS Frontend

A007150 2-part of number of tournaments on n nodes.

%I A007150 M0269 #34 Jul 02 2024 16:04:01
%S A007150 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,
%T A007150 17,15,19,16,20,17,19,18,19,19,26,20,22,21,23,22,23,23,30,24,26,25,28,
%U A007150 26,27,27,30,28,30,29,33,30,31,31,35,32,34,33,38,34,37,35,38,36,38,37,39
%N A007150 2-part of number of tournaments on n nodes.
%D A007150 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007150 Chai Wah Wu, <a href="/A007150/b007150.txt">Table of n, a(n) for n = 1..141</a>
%H A007150 Steven C. Cater and Robert W. Robinson, <a href="http://cobweb.cs.uga.edu/~rwr/publications/techtournament.pdf">Exponents of 2 in the numbers of unlabeled graphs and tournaments</a>, Congressus Numerantium, 82 (1991), pp. 139-155.
%H A007150 Steven C. Cater and Robert W. Robinson, <a href="/A007149/a007149.pdf">Exponents of 2 in the numbers of unlabeled graphs and tournaments</a>, Preprint. (Annotated scanned copy)
%H A007150 <a href="/index/To#tournament">Index entries for sequences related to tournaments</a>
%F A007150 a(n) = A007814(A000568(n)). - _Michel Marcus_, Jan 06 2020
%t A007150 A000568 = Cases[Import["https://oeis.org/A000568/b000568.txt", "Table"], {_, _}][[All, 2]];
%t A007150 IntegerExponent[#, 2]& /@ A000568 // Rest (* _Jean-François Alcover_, Jan 06 2020 *)
%o A007150 (Python)
%o A007150 from itertools import product
%o A007150 from math import prod, factorial, gcd
%o A007150 from fractions import Fraction
%o A007150 from sympy.utilities.iterables import partitions
%o A007150 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
%Y A007150 Power of 2 dividing A000568(n). Cf. A007814.
%K A007150 nonn
%O A007150 1,4
%A A007150 _N. J. A. Sloane_
%E A007150 More terms from A000568 by _Jean-François Alcover_, Jan 06 2020