A357286 a(n) = (1/8)*A357285.

0, 0, 0, 0, 0, 0, 0, 1, 4, 13, 38, 99, 240, 565, 1274, 2799, 6052, 12857, 26958, 56099, 115704, 237133, 484002, 983543, 1992012, 4026017, 8118262, 16342347, 32860832, 65998837, 132437322, 265603743, 532348916, 1066505545, 2135992990, 4276649971, 8560661832

Offset: 0

Author

Clark Kimberling, Oct 02 2022

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A357285.

Programs

Mathematica

s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
a[n_] := Select[s[n], #[[1]] + #[[2]] + #[[3]] < #[[-1]] &]
(1/8)*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^7/((-1 + x)^2 (-1 + 2 x) (-1 + 2 x^2) (-1 + 4 x^3))).