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

0,1

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

Links

Table of n, a(n) for n=0..43.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

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.

From Amiram Eldar, Oct 19 2025: (Start)

Sum_{n>=0} 1/a(n) = 3873307/10930920.

Sum_{n>=0} (-1)^n/a(n) = 12*log(2)/13 - 5282411/10930920. (End)

Mathematica

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

Crossrefs

Cf. A056000 (third column), A096942 (fifth column).

Cf. A000292, A096940.

Sequence in context: A358307 A131425 A227720 * A246697 A098404 A190970

Adjacent sequences: A096938 A096939 A096940 * A096942 A096943 A096944

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 16 2004

Status

approved