A095671 Ninth column (m=8) of (1,4)-Pascal triangle A095666.

4, 33, 153, 525, 1485, 3663, 8151, 16731, 32175, 58630, 102102, 171054, 277134, 436050, 668610, 1001946, 1470942, 2119887, 3004375, 4193475, 5772195, 7844265, 10535265, 13996125, 18407025, 23981724, 30972348, 39674668, 50433900

Offset: 0

Author

Wolfdieter Lang, Jun 11 2004

Keywords

• nonn
• easy

Comments

If Y is a 4-subset of an n-set X then, for n>=11, a(n-11) is the number of 8-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Programs

Mathematica

CoefficientList[Series[(4-3x)/(1-x)^9,{x,0,30}],x] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{4,33,153,525,1485,3663,8151,16731,32175},30] (* Harvey P. Dale, Jul 07 2015 *)

Maxima

A095671(n):=(n+32)*binomial(n+7, 7)/8$
makelist(A095671(n),n,0,30); /* Martin Ettl, Nov 03 2012 */

Formula

G.f.: (4-3*x)/(1-x)^9.

a(n) = 4*b(n)-3*b(n-1) =(n+32)*binomial(n+7, 7)/8, with b(n):=binomial(n+8, 8)=A000581(n+8, 8).

a(0)=4, a(1)=33, a(2)=153, a(3)=525, a(4)=1485, a(5)=3663, a(6)=8151, a(7)=16731, a(8)=32175, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Jul 07 2015