OFFSET
0,8
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-1,-2,-1,1,3,-2).
FORMULA
a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) + 3*a(n-6) - 2*a(n-7).
G.f.: x^6/((-1 + x)^3 (1 + x) (-1 + 2 x) (1 + x + x^2)).
a(n) ~ A021025*2^n. - Stefano Spezia, Oct 03 2022
a(n) = 2^n/21 - n^2/12 + n/6 + O(1). Conjecture: a(n) = round(2^n/21 - n^2/12 + n/6). - Charles R Greathouse IV, Oct 11 2022
EXAMPLE
The 3 relevant subsets of {1,2,3,4,5,6,7} are {1, 2, 6}, {1, 2, 7}, {1, 2, 3, 7}.
MATHEMATICA
s[n_] := s[n] = Select[Subsets[Range[n]], Length[#] >= 3 &];
a[n_] := Select[s[n], #[[1]] + #[[2]] < #[[-1]] - #[[-2]] &]
Table[Length[a[n]], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 02 2022
STATUS
approved