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

Offset

2,1

References

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).

Links

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)

Prog

(PARI)
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

Crossrefs

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

Sequence in context: A318634 A006713 A248362 * A248361 A345027 A203428

Adjacent sequences: A006709 A006710 A006711 * A006713 A006714 A006715

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved