cp's OEIS Frontend

A185355 Number of n X n symmetric (0,1)-matrices containing four ones.

%I A185355 #28 Jul 02 2020 10:46:18
%S A185355 0,1,12,52,150,345,686,1232,2052,3225,4840,6996,9802,13377,17850,
%T A185355 23360,30056,38097,47652,58900,72030,87241,104742,124752,147500,
%U A185355 173225,202176,234612,270802,311025,355570,404736,458832,518177,583100,653940,731046,814777
%N A185355 Number of n X n symmetric (0,1)-matrices containing four ones.
%C A185355 Based on equation (11) from the Cameron et al., reference.
%H A185355 G. C. Greubel, <a href="/A185355/b185355.txt">Table of n, a(n) for n = 1..1000</a>
%H A185355 P. Cameron, T. Prellberg and D. Stark, <a href="https://doi.org/10.37236/1111">Asymptotics for incidence matrix classes</a>, Electron. J. Combin. 13 (2006), #R85, p. 11.
%F A185355 a(n) = Sum_{k=0..2} C(C(n,2),k)*C(n,4-2*k).
%F A185355 a(n) = n^2*(n-1)*(5*n-7)/12.
%F A185355 G.f.: x^2*(1+7*x+2*x^2)/(1-x)^5.
%p A185355 a:= n-> (7+(5*n-12)*n)*n^2/12:
%p A185355 seq (a(n), n=1..40);
%t A185355 Table[n^2*(n - 1)*(5*n - 7)/12, {n, 1, 50}] (* _G. C. Greubel_, Jun 28 2017 *)
%o A185355 (PARI) for(n=1,25, print1(n^2*(n-1)*(5*n-7)/12, ", ")) \\ _G. C. Greubel_, Jun 28 2017
%Y A185355 Cf. A002378, A006331.
%Y A185355 Column m=4 of A184948.
%K A185355 nonn
%O A185355 1,3
%A A185355 _L. Edson Jeffery_, Feb 29 2012