A357285 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).

0, 0, 0, 0, 0, 0, 0, 8, 32, 104, 304, 792, 1920, 4520, 10192, 22392, 48416, 102856, 215664, 448792, 925632, 1897064, 3872016, 7868344, 15936096, 32208136, 64946096, 130738776, 262886656, 527990696, 1059498576, 2124829944, 4258791328, 8532044360, 17087943920

Offset

0,8

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (4, -3, -2, -6, 8, 24, -40, 16).

Formula

a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3) - 6*a(n-4) + 8*a(n-5) + 24*a(n-6) - 40*a(n-7).

G.f.: -((8 x^7)/((-1 + x)^2 (-1 + 2 x) (-1 + 2 x^2) (-1 + 4 x^3))).

Example

The 8 relevant subsets of {1,2,3,4,5,6,7} are {1,2,3,7}, {1,2,3,4,7}, {1,2,3,5,7}, {1,2,3,6,7}, {1,2,3,4,5,7}, {1,2,3,4,6,7}, {1,2,3,5,6,7}, and {1,2,3,4,5,6,7}.

Mathematica

s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
a[n_] := Select[s[n], #[[1]] + #[[2]] + #[[3]] < #[[-1]] &]
Table[Length[a[n]], {n, 0, 18}]

Crossrefs

Cf. A357286, A357287, A357289.

Sequence in context: A195590 A071345 A178797 * A100312 A302507 A204643

Adjacent sequences: A357282 A357283 A357284 * A357286 A357287 A357288

Keyword

nonn,easy

Author

Clark Kimberling, Oct 02 2022

Status

approved