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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.
(Formerly M2603 N1030)
3
1, 3, 6, 42, 618, 15990, 668526, 43558242, 4373213298, 677307561630, 162826875512646, 61183069270120842, 36134310487980825258, 33673533885068169649830, 49646105434209446798290206, 116002075479856331220877149042, 430053223599741677879550609246498, 2531493110297317758855120762121050990
OFFSET
0,2
REFERENCES
R. C. Read, personal communication.
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
R. C. Read, E. M. Wright, Colored graphs: A correction and extension, Canad. J. Math. 22 1970 594-596.
FORMULA
E.g.f.: log(A(x))+1 where A(x) is the e.g.f. for A191371. - Geoffrey Critzer, Jun 02 2011
a(n) = m_n(3) using the functions defined in A002032. - Sean A. Irvine, May 29 2013
Logarithmic transform of A191371. - Andrew Howroyd, Dec 03 2018
MATHEMATICA
f[{k_, r_, m_}]:= Binomial[m+r+k, k] Binomial[m+r, r] 2^(k r +k m + r m);
a = Sum[Total[Map[f, Compositions[n, 3]]] x^n/n!, {n, 0, 20}];
Range[0, 20]! CoefficientList[Series[Log[a]+1, {x, 0, 20}], x] (* Geoffrey Critzer, Jun 02 2011 *)
PROG
(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
CROSSREFS
Column k=3 of A322279.
Sequence in context: A079095 A125889 A300599 * A202858 A116315 A363475
KEYWORD
nonn
STATUS
approved