cp's OEIS Frontend

A002029 Number of connected graphs on n labeled nodes, each node being colored with one of 4 colors, such that no edge joins nodes of the same color.

%I A002029 M3459 N1406 #36 Sep 05 2019 00:04:46
%S A002029 1,4,12,132,3156,136980,10015092,1199364852,234207001236,
%T A002029 75018740661780,39745330657406772,35073541377640231092,
%U A002029 51798833078501480220756,128412490016744675540378580,535348496386845235339961362932,3757366291145650829115977555259252
%N A002029 Number of connected graphs on n labeled nodes, each node being colored with one of 4 colors, such that no edge joins nodes of the same color.
%D A002029 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002029 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A002029 R. C. Read, personal communication.
%H A002029 Andrew Howroyd, <a href="/A002029/b002029.txt">Table of n, a(n) for n = 0..50</a>
%H A002029 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 A002029 E.g.f.: log(b(x)+1)+1 where b(x) = 4 * e.g.f. of A000686. - _Sean A. Irvine_, May 27 2013
%F A002029 a(n) = m_n(4) using the functions defined in A002032. - _Sean A. Irvine_, May 29 2013
%F A002029 Logarithmic transform of A223887. - _Andrew Howroyd_, Dec 03 2018
%t A002029 m = 16;
%t A002029 serconv = (CoefficientList[Sum[x^j*2^Binomial[j, 2], {j, 0, m}] + O[x]^m, x]*CoefficientList[(Sum[x^j/(j!*2^Binomial[j, 2]), {j, 0, m}] + O[x]^m)^4, x]) . x^Range[0, m-1];
%t A002029 CoefficientList[1 + Log[serconv] + O[x]^m, x]*Range[0, m-1]! (* _Jean-François Alcover_, Sep 04 2019, after _Andrew Howroyd_ *)
%o A002029 (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))^4))))} \\ _Andrew Howroyd_, Dec 03 2018
%Y A002029 Column k=4 of A322279.
%Y A002029 Cf. A002032.
%K A002029 nonn
%O A002029 0,2
%A A002029 _N. J. A. Sloane_
%E A002029 More terms from _Sean A. Irvine_, May 27 2013
%E A002029 Name clarified and offset corrected by _Andrew Howroyd_, Dec 03 2018