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A357292 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 A357292 #9 Oct 23 2022 23:45:38
%S A357292 0,0,0,0,0,1,2,5,11,23,47,96,193,388,778,1558,3118,6239,12480,24963,
%T A357292 49929,99861,199725,399454,798911,1597826,3195656,6391316,12782636,
%U A357292 25565277,51130558,102261121,204522247,409044499,818089003,1636178012,3272356029
%N A357292 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 A357292 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-1,-2,-1,2).
%F A357292 a(n) = 2*a(n-1) + a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6).
%F A357292 G.f.: -(x^5/((-1 + x)^2 (1 + x) (-1 + 2 x) (1 + x + x^2))).
%e A357292 The 2 relevant subsets of {1,2,3,4,5,6} are {1, 2, 5} and {1,2,3,6}.
%t A357292 s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
%t A357292 a[n_] := Select[s[n], #[[1]] + #[[2]] == #[[-1]] - #[[-2]] &]
%t A357292 Table[Length[a[n]], {n, 0, 16}]
%Y A357292 Cf. A357290, A357291.
%K A357292 nonn,easy
%O A357292 0,7
%A A357292 _Clark Kimberling_, Oct 02 2022