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).

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

Author

Clark Kimberling, Oct 02 2022

Keywords

• nonn
• easy

Examples

			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}.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3, -1, -1, -6, 2, 20, -24, 8).

Crossrefs

Cf. A357287, A357290.

Programs

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}]

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)).