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A000662 Number of relations with 3 arguments on n nodes.
(Formerly M2180 N0872)
7
2, 136, 22377984, 768614354122719232, 354460798875983863749270670915141632, 146267071761884981524915186989628577728537526896649216991428608 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
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]
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
PROG
(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<<sum(r*s*t//lcm(r, s, t)*p[r]*p[s]*p[t] for r, s, t in product(p.keys(), repeat=3)), prod(q**p[q]*factorial(p[q]) for q in p)) for p in partitions(n))) # Chai Wah Wu, Jul 02 2024
CROSSREFS
Sequence in context: A226118 A216030 A216083 * A139907 A195379 A221227
KEYWORD
nonn,nice
AUTHOR
STATUS
approved

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Last modified July 25 01:41 EDT 2024. Contains 374585 sequences. (Running on oeis4.)