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A357290 a(n) = number of subsets S of {1,2,...,n} having more than 2 elements such that (sum of least two elements of S) > difference between greatest two elements of S.

%I A357290 #7 Oct 02 2022 13:33:51
%S A357290 0,0,0,1,5,15,39,91,200,424,879,1796,3639,7334,14734,29545,59179,
%T A357290 118459,237033,474195,948534,1897228,3794633,7589460,15179133,
%U A357290 30358498,60717248,121434769,242869833,485739983,971480307,1942960979,3885922348,7771845112
%N A357290 a(n) = number of subsets S of {1,2,...,n} having more than 2 elements such that (sum of least two elements of S) > difference between greatest two elements of S.
%H A357290 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-2,-1,1,3,-2).
%F A357290 a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) + 3*a(n-6) - 2*a(n-7).
%F A357290 G.f.: (x^3 (1 + 2 x + x^2 + x^3))/((-1 + x)^3 (1 + x) (-1 + 2 x) (1 + x + x^2)).
%e A357290 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 A357290 s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
%t A357290 a[n_] := Select[s[n], #[[1]] + #[[2]] > #[[-1]] - #[[-2]] &]
%t A357290 Table[Length[a[n]], {n, 0, 15}]
%Y A357290 Cf. A357291, A357292.
%K A357290 nonn,easy
%O A357290 0,5
%A A357290 _Clark Kimberling_, Oct 02 2022