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A357285
a(n) = number of subsets S of {1,2,...,n} having more than 2 elements such that (sum of least three elements of S) < max(S).
2
0, 0, 0, 0, 0, 0, 0, 8, 32, 104, 304, 792, 1920, 4520, 10192, 22392, 48416, 102856, 215664, 448792, 925632, 1897064, 3872016, 7868344, 15936096, 32208136, 64946096, 130738776, 262886656, 527990696, 1059498576, 2124829944, 4258791328, 8532044360, 17087943920
OFFSET
0,8
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