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.

0, 0, 0, 1, 5, 15, 39, 91, 200, 424, 879, 1796, 3639, 7334, 14734, 29545, 59179, 118459, 237033, 474195, 948534, 1897228, 3794633, 7589460, 15179133, 30358498, 60717248, 121434769, 242869833, 485739983, 971480307, 1942960979, 3885922348, 7771845112

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,-2,-1,1,3,-2).

Crossrefs

Cf. A357291, A357292.

Programs

Mathematica

s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
a[n_] := Select[s[n], #[[1]] + #[[2]] > #[[-1]] - #[[-2]] &]
Table[Length[a[n]], {n, 0, 15}]

Formula

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).

G.f.: (x^3 (1 + 2 x + x^2 + x^3))/((-1 + x)^3 (1 + x) (-1 + 2 x) (1 + x + x^2)).