cp's OEIS Frontend

A002028 Number of connected graphs on n labeled nodes, each node being colored with one of 3 colors, such that no edge joins nodes of the same color.

%I A002028 M2603 N1030 #35 Dec 03 2018 17:46:21
%S A002028 1,3,6,42,618,15990,668526,43558242,4373213298,677307561630,
%T A002028 162826875512646,61183069270120842,36134310487980825258,
%U A002028 33673533885068169649830,49646105434209446798290206,116002075479856331220877149042,430053223599741677879550609246498,2531493110297317758855120762121050990
%N A002028 Number of connected graphs on n labeled nodes, each node being colored with one of 3 colors, such that no edge joins nodes of the same color.
%D A002028 R. C. Read, personal communication.
%D A002028 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002028 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002028 Andrew Howroyd, <a href="/A002028/b002028.txt">Table of n, a(n) for n = 0..50</a>
%H A002028 R. C. Read, E. M. Wright, <a href="http://dx.doi.org/10.4153/CJM-1970-066-1">Colored graphs: A correction and extension</a>, Canad. J. Math. 22 1970 594-596.
%F A002028 E.g.f.: log(A(x))+1 where A(x) is the e.g.f. for A191371. - _Geoffrey Critzer_, Jun 02 2011
%F A002028 a(n) = m_n(3) using the functions defined in A002032. - _Sean A. Irvine_, May 29 2013
%F A002028 Logarithmic transform of A191371. - _Andrew Howroyd_, Dec 03 2018
%t A002028 f[{k_, r_, m_}]:= Binomial[m+r+k, k] Binomial[m+r, r] 2^(k r +k m + r m);
%t A002028   a = Sum[Total[Map[f, Compositions[n, 3]]] x^n/n!, {n, 0, 20}];
%t A002028   Range[0, 20]! CoefficientList[Series[Log[a]+1, {x, 0, 20}], x] (* _Geoffrey Critzer_, Jun 02 2011 *)
%o A002028 (PARI) seq(n)={Vec(serlaplace(1 + log(serconvol(sum(j=0, n, x^j*2^binomial(j, 2)) + O(x*x^n), (sum(j=0, n, x^j/(j!*2^binomial(j, 2))) + O(x*x^n))^3))))} \\ _Andrew Howroyd_, Dec 03 2018
%Y A002028 Column k=3 of A322279.
%Y A002028 Cf. A002031, A002032.
%K A002028 nonn
%O A002028 0,2
%A A002028 _N. J. A. Sloane_