OFFSET
0,1
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).
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
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 *)
PROG
(Maxima) A095671(n):=(n+32)*binomial(n+7, 7)/8$
makelist(A095671(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 11 2004
STATUS
approved