A095663 Eighth column (m=7) of (1,3)-Pascal triangle A095660.

3, 22, 92, 288, 750, 1716, 3564, 6864, 12441, 21450, 35464, 56576, 87516, 131784, 193800, 279072, 394383, 547998, 749892, 1012000, 1348490, 1776060, 2314260, 2985840, 3817125, 4838418, 6084432, 7594752, 9414328, 11594000, 14191056, 17269824, 20902299, 25168806

Offset

0,1

Comments

If Y is a 3-subset of an n-set X then, for n >= 9, a(n-9) is the number of 7-subsets of X having at most one element in common with Y. - Milan Janjic, Nov 23 2007

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

G.f.: (3-2*x)/(1-x)^8.

a(n) = binomial(n+6, 6)*(n+21)/7 = 3*b(n)-2*b(n-1), with b(n) = binomial(n+7, 7); cf. A000580.

From Amiram Eldar, Oct 21 2025: (Start)

Sum_{n>=0} 1/a(n) = 170012461841/429668553600.

Sum_{n>=0} (-1)^n/a(n) = 124544*log(2)/1615 - 13703996049239/257801132160. (End)

Mathematica

a[n_] := Binomial[n+6, 6] * (n+21)/7; Array[a, 30, 0] (* Amiram Eldar, Oct 21 2025 *)

Crossrefs

Cf. A095662 (seventh column), A095664 (ninth column).

Cf. A000580, A095660.

Sequence in context: A302272 A302723 A383637 * A254332 A009029 A009032

Adjacent sequences: A095660 A095661 A095662 * A095664 A095665 A095666

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 11 2004

Status

approved