A096943 Sixth column of (1,5)-Pascal triangle A096940.

5, 26, 81, 196, 406, 756, 1302, 2112, 3267, 4862, 7007, 9828, 13468, 18088, 23868, 31008, 39729, 50274, 62909, 77924, 95634, 116380, 140530, 168480, 200655, 237510, 279531, 327236, 381176, 441936, 510136, 586432, 671517, 766122, 871017, 987012

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>=9, a(n-9) is the number of 5-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007

Links

• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Crossrefs

Fifth column: A096942; seventh column: A096944.

Programs

Mathematica

CoefficientList[Series[(5-4x)/(1-x)^6,{x,0,40}],x] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{5,26,81,196,406,756},40] (* Harvey P. Dale, Jan 11 2014 *)

Formula

G.f.: (5-4*x)/(1-x)^6.

a(n)= (n+25)*binomial(n+4, 4)/5 = 5*b(n)-4*b(n-1), with b(n):= A000389(n+5)=binomial(n+5, 5).

a(0)=5, a(1)=26, a(2)=81, a(3)=196, a(4)=406, a(5)=756, a(n)=6*a(n-1)- 15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, Jan 11 2014