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

0,5

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-2,-1,1,3,-2).

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)).

Example

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}.

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}]

Crossrefs

Cf. A357291, A357292.

Sequence in context: A075717 A062487 A084447 * A099035 A262295 A034182

Adjacent sequences: A357287 A357288 A357289 * A357291 A357292 A357293

Keyword

nonn,easy

Author

Clark Kimberling, Oct 02 2022

Status

approved