OFFSET
0,4
LINKS
FORMULA
a(n) = 2^n - A068911(n).
From Alois P. Heinz, Aug 30 2024: (Start)
G.f.: 2*x^3/((2*x-1)*(3*x^2-1)).
a(n) = 2 * A167762(n-1) for n>=1. (End)
EXAMPLE
The a(1) = 0 through a(5) = 14 subsets:
. . {1,2} {1,3} {1,4}
{1,2,3} {1,2,3} {2,3}
{1,3,4} {1,2,3}
{1,2,3,4} {1,2,4}
{1,3,4}
{1,4,5}
{2,3,4}
{2,3,5}
{1,2,3,4}
{1,2,3,5}
{1,2,4,5}
{1,3,4,5}
{2,3,4,5}
{1,2,3,4,5}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], MemberQ[Total/@Subsets[#, {2}], n]&]], {n, 0, 10}]
PROG
(Python)
def A365544(n): return (1<<n) - (3**(n>>1)<<1 if n&1 else 3**(n-1>>1)<<2) if n else 0 # Chai Wah Wu, Aug 30 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gus Wiseman, Sep 20 2023
STATUS
approved