A065889 a(n) = number of unicyclic connected simple graphs whose cycle has length 4.

3, 60, 1080, 20580, 430080, 9920232, 252000000, 7015381560, 212840939520, 6998969586180, 248180493969408, 9445533398437500, 384213343210045440, 16639691095281974160, 764619269867445288960, 37163398969133506235952, 1905131520000000000000000

Offset: 4

Author

Len Smiley, Nov 27 2001

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..150

Crossrefs

A065888 ( = 2*A065889) counts sagittal graphs with one cycle (length 4).

A column of A098909, A053507.

Main diagonal of A144209.

Cf. A053508.

Programs

GAP

List([4..25], n-> 12*Binomial(n,4)*n^(n-5)); # G. C. Greubel, May 16 2019

Magma

[12*Binomial(n,4)*n^(n-5) : n in [4..25]]; // G. C. Greubel, May 16 2019

Mathematica

Table[12*Binomial[n,4]*n^(n-5), {n,4,25}] (* G. C. Greubel, May 16 2019 *)

PARI

{a(n) = 12*binomial(n,4)*n^(n-5)}; \\ G. C. Greubel, May 16 2019

Sage

[12*binomial(n,4)*n^(n-5) for n in (4..25)] # G. C. Greubel, May 16 2019

Formula

E.g.f.: T^4/8, where T = T(x) is Euler's tree function (see A000169).

a(n) = (n-1)*(n-2)*(n-3)*n^(n-4)/2. - Vladeta Jovovic, Oct 26 2004

a(n) = 3 * A053508(n). - Alois P. Heinz, Jan 09 2025