OFFSET
0,8
LINKS
Index entries for linear recurrences with constant coefficients, signature (4, -3, -2, -6, 8, 24, -40, 16).
FORMULA
a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3) - 6*a(n-4) + 8*a(n-5) + 24*a(n-6) - 40*a(n-7).
G.f.: -((8 x^7)/((-1 + x)^2 (-1 + 2 x) (-1 + 2 x^2) (-1 + 4 x^3))).
EXAMPLE
The 8 relevant subsets of {1,2,3,4,5,6,7} are {1,2,3,7}, {1,2,3,4,7}, {1,2,3,5,7}, {1,2,3,6,7}, {1,2,3,4,5,7}, {1,2,3,4,6,7}, {1,2,3,5,6,7}, and {1,2,3,4,5,6,7}.
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, 18}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 02 2022
STATUS
approved