OFFSET
0,5
LINKS
Index entries for linear recurrences with constant coefficients, signature (3, -1, -1, -6, 2, 20, -24, 8).
FORMULA
a(n) = 3*a(n-1) - a(n-2) - a(n-3) - 6*a(n-4) + 2*a(n-5) + 20*a(n-6) - 24*a(n-7) + 8*a(n-8).
G.f.: (x^3 (-1 - 2 x - 2 x^2 + 4 x^3 + 4 x^4))/((-1 + x)^3 (-1 + 2 x^2) (-1 + 4 x^3)).
EXAMPLE
The 5 relevant subsets of {1,2,3,4} are {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, and {1, 2, 3, 4}.
MATHEMATICA
s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
a[n_] := Select[s[n], #[[1]] + #[[2]] + #[[3]] > #[[-1]] &]
Table[Length[a[n]], {n, 0, 16}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 02 2022
STATUS
approved