A065889 - OEIS

%I #16 Sep 08 2022 08:45:04

%S 3,60,1080,20580,430080,9920232,252000000,7015381560,212840939520,

%T 6998969586180,248180493969408,9445533398437500,384213343210045440,

%U 16639691095281974160,764619269867445288960,37163398969133506235952

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

%H Alois P. Heinz, <a href="/A065889/b065889.txt">Table of n, a(n) for n = 4..150</a>

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

%F a(n) = (n-1)*(n-2)*(n-3)*n^(n-4)/2. - _Vladeta Jovovic_, Oct 26 2004

%t Table[12*Binomial[n,4]*n^(n-5), {n,4,25}] (* _G. C. Greubel_, May 16 2019 *)

%o (PARI) {a(n) = 12*binomial(n,4)*n^(n-5)}; \\ _G. C. Greubel_, May 16 2019

%o (Magma) [12*Binomial(n,4)*n^(n-5) : n in [4..25]]; // _G. C. Greubel_, May 16 2019

%o (Sage) [12*binomial(n,4)*n^(n-5) for n in (4..25)] # _G. C. Greubel_, May 16 2019

%o (GAP) List([4..25], n-> 12*Binomial(n,4)*n^(n-5)) # _G. C. Greubel_, May 16 2019

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

%Y A column of A098909, A053507.

%Y Main diagonal of A144209.

%K nonn

%O 4,1

%A _Len Smiley_, Nov 27 2001