A357284 a(n) = (1/2)*A357283(n).

0, 0, 0, 0, 1, 4, 13, 34, 83, 188, 413, 878, 1839, 3792, 7761, 15762, 31891, 64276, 129301, 259606, 520727, 1043480, 2090009, 4184090, 8374299, 16756764, 33525789, 67067934, 134160415, 268353568, 536756257, 1073578018, 2147254307, 4294639652, 8589475877

Offset: 0

Author

Clark Kimberling, Sep 27 2022

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-3,-6,10,-4).

Crossrefs

Cf. A357283, A274230.

Programs

Mathematica

s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 2 &];  (* note size >=2 *)
a[n_] := Select[s[n], #[[2]] + #[[1]] < #[[-1]] &]
(1/2)Table[Length[a[n]], {n, 0, 18}]

Formula

a(n) = 4*a(n-1) - 3*a(n-2) - 6*a(n-3) + 10*a(n-4) - 4*a(n-5).

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

a(n) = Sum_{i=0..n-2} A274230(i). - Ivan N. Ianakiev, Nov 08 2022