A007149 2-part of number of graphs on n nodes. (Formerly M0017)

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

Offset

0,4

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 = 0..97

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)

Formula

a(n) = A007814(A000088(n)). - Michel Marcus, Jan 06 2020

Mathematica

A000088 = Cases[Import["https://oeis.org/A000088/b000088.txt", "Table"], {_, _}][[All, 2]];
IntegerExponent[#, 2]& /@ A000088 (* Jean-François Alcover, Jan 06 2020 *)

Prog

(Python)
from itertools import combinations
from math import prod, factorial, gcd
from fractions import Fraction
from sympy.utilities.iterables import partitions
def A007149(n): return (~(m:=int(sum(Fraction(1<<sum(p[r]*p[s]*gcd(r, s) for r, s in combinations(p.keys(), 2))+sum((q>>1)*r+(q*r*(r-1)>>1) for q, r in p.items()), prod(q**r*factorial(r) for q, r in p.items())) for p in partitions(n)))) & m-1).bit_length() # Chai Wah Wu, Jul 02 2024

Crossrefs

Power of 2 dividing A000088. Cf. A007814.

Sequence in context: A065051 A084665 A035392 * A028832 A260411 A199331

Adjacent sequences: A007146 A007147 A007148 * A007150 A007151 A007152

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Aug 15 2019

Status

approved