0,3

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

CRC Handbook of Combinatorial Designs, 1996, p. 651.

R. L. Davies, The numbers of structures of finite relations, Proc. Amer. Math. Soc., 4 (1953), 486-494.

F. Harary, Graph Theory. Addison-Wesley, Reading, MA, 1969, p. 225.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 124, Table 5.1.2 and p. 241, Table A4.

M. D. McIlroy, Calculation of numbers of structures of relations on finite sets, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sept. 15, 1955, pp. 14-22.

W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 522.

Keith Briggs, Table of n, a(n) for n = 0..64

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.

L. Travis, [math/9811127] Graphical Enumeration: A Species-Theoretic Approach

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for "core" sequences

(Maple code from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 06 2006) with(combinat):with(numtheory):

for n from 1 to 20 do p:=partition(n):

s:=0:for k from 1 to nops(p) do

q:=convert(p[k], multiset):

for i from 1 to n do a(i):=0:od:for i from 1 to nops(q) do a(q[i][1]):=q[i][2]:od:

c:=1:ord:=1:for i from 1 to n do c:=c*a(i)!*i^a(i): if a(i)<>0 then ord:=lcm(ord, i):fi:od:

g:=0:for d from 1 to ord do if ord mod d=0 then g1:=0:for del from 1 to d do if del<=n and d mod del=0 then g1:=g1+del*a(del):fi:od:g:=g+phi(ord/d)*g1*(g1-1):fi:od:

s:=s+2^(g/ord)/c:

od:

print(n, s):

od:

Sequence in context: A007006 A166860 A113597 this_sequence A071897 A013923 A053466

Adjacent sequences: A000270 A000271 A000272 this_sequence A000274 A000275 A000276

nonn,core,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 14 1999