Search: id:A000685
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%I A000685 M3995 N1656
%S A000685 1,5,41,545,11681,402305,22207361,1961396225,276825510401,
%T A000685 62368881977345,22413909724518401,12840603873823473665,
%U A000685 11720394922432296755201,17037597932370037286600705
%N A000685 Number of 3-colored labeled graphs on n nodes.
%C A000685 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
%D A000685 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000685 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000685 R. C. Read, The number of k-colored graphs on labeled nodes, Canad. J. 
               Math., 12 (1960), 410-414.
%D A000685 R. C. Read, personal communication.
%H A000685 T. D. Noe, <a href="b000685.txt">Table of n, a(n) for n=1..50</a>
%H A000685 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Bipartite, k-colorable 
               and k-colored graphs</a> (3*A000685)
%F 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
%p A000685 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);
%Y A000685 Cf. A000683, A047863.
%Y A000685 Sequence in context: A143415 A056545 A009755 this_sequence A144286 A139034 
               A073854
%Y A000685 Adjacent sequences: A000682 A000683 A000684 this_sequence A000686 A000687 
               A000688
%K A000685 nonn,easy,nice
%O A000685 1,2
%A A000685 N. J. A. Sloane (njas(AT)research.att.com).
%E A000685 More terms from Pab Ter (pabrlos(AT)yahoo.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               May 05 2004

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