OFFSET
0,1
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).
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
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 11 2004
STATUS
approved