A357288 a(n) = (1/4)*A357287(n).

0, 0, 0, 0, 0, 0, 1, 2, 5, 12, 23, 42, 85, 144, 251, 454, 753, 1244, 2183, 3506, 5725, 9736, 15539, 24926, 41993, 66228, 105823, 176138, 277173, 439648, 729099, 1141430, 1807713, 2981900, 4663991, 7361890, 12124173, 18918072, 29840739, 49020942

Offset: 0

Author

Clark Kimberling, Oct 02 2022

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,0,-6,-4,16,-8).

Crossrefs

Cf. A357287.

Programs

Mathematica

s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
a[n_] := Select[s[n], #[[1]] + #[[2]] + #[[3]] == #[[-1]] &]
(1/4)*Table[Length[a[n]], {n, 0, 15}]

Formula

a(n) = 2*a(n-1) + a(n-2) - 6*a(n-4) - 4*a(n-5) + 16*a(n-6) - 8*a(n-7).

G.f.: x^6/((-1 + x)^2 (-1 + 2 x^2) (-1 + 4 x^3)).