login
A185355
Number of n X n symmetric (0,1)-matrices containing four ones.
1
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
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
Column m=4 of A184948.
Sequence in context: A045219 A325379 A054410 * A339029 A297757 A223249
KEYWORD
nonn
AUTHOR
L. Edson Jeffery, Feb 29 2012
STATUS
approved