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A357289
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, 1, 5, 16, 38, 83, 167, 314, 572, 1021, 1757, 3004, 5082, 8439, 13971, 23086, 37576, 61281, 99833, 160912, 259878, 420283, 672847, 1081058, 1739124, 2774021, 4439701, 7121188, 11326386, 18087487, 28944587, 45962070, 73268704, 117090409, 185684721, 295697784, 472033278, 747983491
OFFSET
0,5
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
Sequence in context: A211807 A174723 A011932 * A131283 A082199 A082190
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 02 2022
STATUS
approved