A000662 Number of relations with 3 arguments on n nodes.

2, 136, 22377984, 768614354122719232, 354460798875983863749270670915141632, 146267071761884981524915186989628577728537526896649216991428608

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

References

• F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 76 (2.2.31)
• W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..15
• P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
• W. Oberschelp, Strukturzahlen in endlichen Relationssystemen, in Contributions to Mathematical Logic (Proceedings 1966 Hanover Colloquium), pp. 199-213, North-Holland Publ., Amsterdam, 1968. [Annotated scanned copy]

Crossrefs

Cf. A000595, A001377, A051241.

Programs

Python

from itertools import product
from math import factorial, prod, lcm
from fractions import Fraction
from sympy.utilities.iterables import partitions
def A000662(n): return int(sum(Fraction(1<Chai Wah Wu, Jul 02 2024

Formula

a(n) = Sum_{1*s_1+2*s_2+...=n} (fixA[s_1, s_2,...]/(1^s_1*s_1!*2^s_2*s_2!*...)) where fixA[s_1, s_2, ...] = 2^Sum_{i, j, k>=1} (i*j*k*s_i*s_j*s_k/lcm(i, j, k)). - Christian G. Bower, Jan 06 2004