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

4,1

Links

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

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

Mathematica

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

Prog

(PARI) {a(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
(Sage) [12*binomial(n, 4)*n^(n-5) for n in (4..25)] # G. C. Greubel, May 16 2019
(GAP) List([4..25], n-> 12*Binomial(n, 4)*n^(n-5)); # G. C. Greubel, May 16 2019

Crossrefs

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

A column of A098909, A053507.

Main diagonal of A144209.

Cf. A053508.

Sequence in context: A378777 A144659 A115490 * A183251 A001084 A137150

Adjacent sequences: A065886 A065887 A065888 * A065890 A065891 A065892

Keyword

nonn,changed

Author

Len Smiley, Nov 27 2001

Status

approved