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 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. (Formerly M3459 N1406) 3
 1, 4, 12, 132, 3156, 136980, 10015092, 1199364852, 234207001236, 75018740661780, 39745330657406772, 35073541377640231092, 51798833078501480220756, 128412490016744675540378580, 535348496386845235339961362932, 3757366291145650829115977555259252 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES 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). R. C. Read, personal communication. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 R. C. Read, E. M. Wright, Colored graphs: A correction and extension, Canad. J. Math. 22 1970 594-596. FORMULA E.g.f.: log(b(x)+1)+1 where b(x) = 4 * e.g.f. of A000686. - Sean A. Irvine, May 27 2013 a(n) = m_n(4) using the functions defined in A002032. - Sean A. Irvine, May 29 2013 Logarithmic transform of A223887. - Andrew Howroyd, Dec 03 2018 MATHEMATICA m = 16; 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]; CoefficientList[1 + Log[serconv] + O[x]^m, x]*Range[0, m-1]! (* Jean-François Alcover, Sep 04 2019, after Andrew Howroyd *) 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))^4))))} \\ Andrew Howroyd, Dec 03 2018 CROSSREFS Column k=4 of A322279. Cf. A002032. Sequence in context: A053551 A009663 A197899 * A204321 A152121 A077611 Adjacent sequences: A002026 A002027 A002028 * A002030 A002031 A002032 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Sean A. Irvine, May 27 2013 Name clarified and offset corrected by Andrew Howroyd, Dec 03 2018 STATUS approved

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Last modified December 9 01:07 EST 2023. Contains 367681 sequences. (Running on oeis4.)