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

0, 1, 12, 52, 150, 345, 686, 1232, 2052, 3225, 4840, 6996, 9802, 13377, 17850, 23360, 30056, 38097, 47652, 58900, 72030, 87241, 104742, 124752, 147500, 173225, 202176, 234612, 270802, 311025, 355570, 404736, 458832, 518177, 583100, 653940, 731046, 814777

Offset: 1

Author

L. Edson Jeffery, Feb 29 2012

Keywords

• nonn

Comments

Based on equation (11) from the Cameron et al., reference.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• P. Cameron, T. Prellberg and D. Stark, Asymptotics for incidence matrix classes, Electron. J. Combin. 13 (2006), #R85, p. 11.

Crossrefs

Cf. A002378, A006331.

Column m=4 of A184948.

Programs

Maple

a:= n-> (7+(5*n-12)*n)*n^2/12:
seq (a(n), n=1..40);

Mathematica

Table[n^2*(n - 1)*(5*n - 7)/12, {n, 1, 50}] (* G. C. Greubel, Jun 28 2017 *)

PARI

for(n=1,25, print1(n^2*(n-1)*(5*n-7)/12, ", ")) \\ G. C. Greubel, Jun 28 2017

Formula

a(n) = Sum_{k=0..2} C(C(n,2),k)*C(n,4-2*k).

a(n) = n^2*(n-1)*(5*n-7)/12.

G.f.: x^2*(1+7*x+2*x^2)/(1-x)^5.