A286757 Number of labeled connected rooted trivalent graphs with 2n nodes.

0, 4, 120, 33600, 18471600, 18386121600, 30231607606200, 76388992266787200, 281063897503929540000, 1444102677105174358272000, 10020068498645397815029407000, 91355440119583548608158042584000, 1069762020017605579789451640683370000

Offset

1,2

Comments

A006607 gives values matching Table 1 (p. 342) of Wormald. However, the values in the table for n > 4 do not appear to match formulas given for generating the table.

References

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.

Links

Table of n, a(n) for n=1..13.

N. C. Wormald, Triangles in labeled cubic graphs, pp. 337-345 of Combinatorial Mathematics (Canberra, 1977), Lect. Notes Math. 686, 1978.

Formula

Let b(0)=b(1)=0, b(n) = 2*binomial(2*n, 2)*b(n-1) + 12*binomial(2*n, 4)*b(n-2) + 6*binomial(2*n, 3)*A002829(n-1) + 60*binomial(2*n, 5)*A002829(n-2) + 1260*binomial(2*n, 7)*A002829(n-3). a(n)=b(n) except a(2)=4.

Let Q(x) be an e.g.f. for A002829: Q(x) = 1 + (1/4!)*x^4 + (70/6!)*x^6 + (19355/8!)*x^8 + ...; then A(x), the e.g.f. for this sequence, satisfies (2 - 2*x^2 - x^4) * (A(x) - (1/6)*x^4) = (2*x^3 + x^5 + (1/2)*x^7) * Q'(x) where Q'(x) is the derivative of Q(x) with respect to x.

Crossrefs

Cf. A002829, A006607.

Sequence in context: A071304 A213957 A006607 * A239187 A062081 A053881

Adjacent sequences: A286754 A286755 A286756 * A286758 A286759 A286760

Keyword

nonn

Author

Sean A. Irvine, May 13 2017

Status

approved