A096941 Fourth column of (1,5)-Pascal triangle A096940.

5, 16, 34, 60, 95, 140, 196, 264, 345, 440, 550, 676, 819, 980, 1160, 1360, 1581, 1824, 2090, 2380, 2695, 3036, 3404, 3800, 4225, 4680, 5166, 5684, 6235, 6820, 7440, 8096, 8789, 9520, 10290, 11100, 11951, 12844, 13780, 14760, 15785, 16856, 17974, 19140

Offset: 0

Author

Wolfdieter Lang, Jul 16 2004

Keywords

• nonn
• easy

Comments

If Y is a 5-subset of an n-set X then, for n>=7, a(n-7) is the number of 3-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007

Crossrefs

Third column: A056000; fifth column: A096942.

Programs

Mathematica

Table[(n^3 + 15 n^2 + 14 n)/6, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)

Formula

a(n)= (n+15)*(n+2)*(n+1)/6 = 5*b(n)-4*b(n-1), with b(n):=A000292(n)=binomial(n+3, 3).

G.f.: (5-4*x)/(1-x)^4.