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

1,3

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.

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.

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 *)

Prog

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

Crossrefs

Cf. A002378, A006331.

Column m=4 of A184948.

Sequence in context: A045219 A325379 A054410 * A339029 A297757 A223249

Adjacent sequences: A185352 A185353 A185354 * A185356 A185357 A185358

Keyword

nonn

Author

L. Edson Jeffery, Feb 29 2012

Status

approved