1,2

Sequence represents 1/3 of the number of 3-colored labeled graphs on n nodes. Indeed, on p. 413 of the Read paper, column 3 is 3,15,123,1635,..; or see A047863. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 06 2004

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).

R. C. Read, The number of k-colored graphs on labeled nodes, Canad. J. Math., 12 (1960), 410-414.

R. C. Read, personal communication.

T. D. Noe, Table of n, a(n) for n=1..50

S. R. Finch, Bipartite, k-colorable and k-colored graphs (3*A000685)

a(n)=(1/3)sum(binomial(n, j)*2^[j(n-j)]*c(j), j=0..n), where c(n)=sum(binomial(n, i)*2^[i(n-i)], i=0..n)=A047863(n) - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 06 2004

c[0]:=1: for n from 1 to 30 do c[n]:=sum(binomial(n, i)*2^(i*(n-i)), i=0..n) od: a:=n->(1/3)*sum(binomial(n, j)*2^(j*(n-j))*c[j], j=0..n): seq(a(n), n=1..19);

Cf. A000683, A047863.

Sequence in context: A143415 A056545 A009755 this_sequence A144286 A139034 A073854

Adjacent sequences: A000682 A000683 A000684 this_sequence A000686 A000687 A000688

nonn,easy,nice

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

More terms from Pab Ter (pabrlos(AT)yahoo.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), May 05 2004