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A006712 Number of 3-edge-colored trivalent graphs with 2n labeled nodes.
(Formerly M4311)
6, 480, 197820, 150474240, 208857587400, 471804812519040, 1625459273858019600, 8112729590064978278400, 56342429224416522460072800, 527075322501595757416502976000, 6466573585901882433727764077860800, 101749747195531624711768653503416320000 (list; graph; refs; listen; history; text; internal format)



R. C. Read, Some Enumeration Problems in Graph Theory. Ph.D. Dissertation, Department of Mathematics, Univ. London, 1958.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Andrew Howroyd, Table of n, a(n) for n = 2..50

Sean A. Irvine, Illustration of initial terms

R. C. Read, Letter to N. J. A. Sloane, Feb 04 1971 (gives initial terms of this sequence)



dpermcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=2*t*k; s+=2*t); s!/m}

S(n, x)={vector(n, n, if(n>1, sum(k=0, n, binomial(2*n-k, k)*2*n/(2*n-k)*x^k), 0))}

q(n, s)={my(t=0); if(n>1, forpart(p=n, t+=dpermcount(p)*prod(i=1, #p, s[p[i]]), [2, n])); t}

a(n)={my(p=q(n, S(n, x))); sum(i=0, poldegree(p), polcoeff(p, n-i)*(-1)^(n-i)*(2*i)!/(2^i*i!))} \\ Andrew Howroyd, Dec 18 2017


Cf. A006713 (for connected cases), A248361 (for the incorrect values). See also A002830, A002831, A005638.

Sequence in context: A318634 A006713 A248362 * A248361 A203428 A264741

Adjacent sequences:  A006709 A006710 A006711 * A006713 A006714 A006715




N. J. A. Sloane


a(5)-a(6) corrected and a(7)-a(10) from Sean A. Irvine, Oct 05 2014

Terms a(11) and beyond from Andrew Howroyd, Dec 18 2017



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Last modified November 24 10:26 EST 2020. Contains 338612 sequences. (Running on oeis4.)