A096945 Eighth column of (1,5)-Pascal triangle A096940.

5, 36, 148, 456, 1170, 2640, 5412, 10296, 18447, 31460, 51480, 81328, 124644, 186048, 271320, 387600, 543609, 749892, 1019084, 1366200, 1808950, 2368080, 3067740, 3935880, 5004675, 6310980, 7896816, 9809888, 12104136, 14840320

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>=11, a(n-11) is the number of 7-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 (8, -28, 56, -70, 56, -28, 8, -1).

Crossrefs

Seventh column: A096944; ninth column: A096946.

Programs

Mathematica

CoefficientList[Series[(5-4*x)/(1-x)^8,{x,0,30}],x] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{5,36,148,456,1170,2640,5412,10296},30] (* Harvey P. Dale, Aug 16 2014 *)

Formula

G.f.: (5-4*x)/(1-x)^8.

a(n)= (n+35)*binomial(n+6, 6)/7 = 5*b(n)-4*b(n-1), with b(n):=A000580(n+7)=binomial(n+7, 7).

a(0)=5, a(1)=36, a(2)=148, a(3)=456, a(4)=1170, a(5)=2640, a(6)=5412, a(7)=10296, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)- 28*a(n-6)+ 8*a(n-7)-a(n-8). - Harvey P. Dale, Aug 16 2014