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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).

%I A357289 #4 Oct 02 2022 13:34:41
%S A357289 0,0,0,1,5,16,38,83,167,314,572,1021,1757,3004,5082,8439,13971,23086,
%T A357289 37576,61281,99833,160912,259878,420283,672847,1081058,1739124,
%U A357289 2774021,4439701,7121188,11326386,18087487,28944587,45962070,73268704,117090409,185684721,295697784,472033278,747983491
%N 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).
%H A357289 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (3, -1, -1, -6, 2, 20, -24, 8).
%F A357289 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).
%F A357289 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)).
%e A357289 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}.
%t A357289 s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
%t A357289 a[n_] := Select[s[n], #[[1]] + #[[2]] + #[[3]] > #[[-1]] &]
%t A357289 Table[Length[a[n]], {n, 0, 16}]
%Y A357289 Cf. A357287, A357290.
%K A357289 nonn,easy
%O A357289 0,5
%A A357289 _Clark Kimberling_, Oct 02 2022