login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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

%I #6 Dec 10 2023 09:24:12

%S 0,0,0,0,0,0,0,1,4,13,38,99,240,565,1274,2799,6052,12857,26958,56099,

%T 115704,237133,484002,983543,1992012,4026017,8118262,16342347,

%U 32860832,65998837,132437322,265603743,532348916,1066505545,2135992990,4276649971,8560661832

%N a(n) = (1/8)*A357285.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4, -3, -2, -6, 8, 24, -40, 16).

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

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

%t s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];

%t a[n_] := Select[s[n], #[[1]] + #[[2]] + #[[3]] < #[[-1]] &]

%t (1/8)*Table[Length[a[n]], {n, 0, 18}]

%Y Cf. A357285.

%K nonn,easy

%O 0,9

%A _Clark Kimberling_, Oct 02 2022