A007149 2-part of number of graphs on n nodes.

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

Author

N. J. A. Sloane

Keywords

• nonn

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)

Crossrefs

Power of 2 dividing A000088. Cf. A007814.

Programs

Mathematica

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

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<>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

Formula

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

Extensions

More terms from Alois P. Heinz, Aug 15 2019