A095662 Seventh column (m=6) of (1,3)-Pascal triangle A095660.

3, 19, 70, 196, 462, 966, 1848, 3300, 5577, 9009, 14014, 21112, 30940, 44268, 62016, 85272, 115311, 153615, 201894, 262108, 336490, 427570, 538200, 671580, 831285, 1021293, 1246014, 1510320, 1819576, 2179672, 2597056, 3078768, 3632475

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>=8, a(n-8) is the number of 6-subsets of X having at most one element in common with Y. - Milan Janjic, Nov 23 2007

Links

• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Crossrefs

Sixth column: A000574. Eighth column: A095663.

Programs

Mathematica

CoefficientList[Series[(3-2x)/(1-x)^7,{x,0,40}],x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{3,19,70,196,462,966,1848},40] (* Harvey P. Dale, Mar 30 2014 *)

Formula

G.f.: (3-2*x)/(1-x)^7.

a(n)= binomial(n+5, 5)*(n+18)/6 = 3*b(n)-2*b(n-1), with b(n):=binomial(n+6, 6); cf. A000579.

a(0)=3, a(1)=19, a(2)=70, a(3)=196, a(4)=462, a(5)=966, a(6)=1848, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Harvey P. Dale, Mar 30 2014