OFFSET
0,1
COMMENTS
If Y is a 3-subset of an n-set X then, for n >= 11, a(n-11) is the number of 9-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 (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = binomial(n+8, 8)*(n+27)/9 = 3*b(n)-2*b(n-1), with b(n) = binomial(n+9, 9); cf. A000582.
G.f.: (3-2*x)/(1-x)^10.
From Amiram Eldar, Oct 21 2025: (Start)
Sum_{n>=0} 1/a(n) = 251436784018857/663871263770000.
Sum_{n>=0} (-1)^n/a(n) = 4490496*log(2)/10925 - 1322567719498684831/4647098846390000. (End)
MATHEMATICA
Table[Binomial[n+8, 8] (n+27)/9, {n, 0, 30}] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {3, 28, 145, 550, 1705, 4576, 11011, 24310, 50050, 97240}, 30] (* Harvey P. Dale, Oct 13 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 11 2004
STATUS
approved