A095664 Ninth column (m=8) of (1,3)-Pascal triangle A095660.

3, 25, 117, 405, 1155, 2871, 6435, 13299, 25740, 47190, 82654, 139230, 226746, 358530, 552330, 831402, 1225785, 1773783, 2523675, 3535675, 4884165, 6660225, 8974485, 11960325, 15777450, 20615868, 26700300, 34295052, 43709380, 55303380, 69494436, 86764260, 107666559, 132835365, 162994065

Offset: 0

Author

Wolfdieter Lang, Jun 11 2004

Keywords

• nonn
• easy

Comments

If Y is a 3-subset of an n-set X then, for n>=10, a(n-10) is the number of 8-subsets of X having at most one element in common with Y. - Milan Janjic, Nov 23 2007

Crossrefs

Eighth column: A095663. Tenth column: A095665.

Programs

PARI

x='x+O('x^66); Vec((3-2*x)/(1-x)^9) \\ Joerg Arndt, May 11 2013

Formula

a(n)= binomial(n+7, 7)*(n+24)/8 = 3*b(n)-2*b(n-1), with b(n):=binomial(n+8, 8); cf. A000581.

G.f.: (3-2*x)/(1-x)^9.