OFFSET
0,2
COMMENTS
In other words, no element is the difference of two consecutive elements.
From David A. Corneth, Aug 02 2023: (Start)
As subsets counted in a(n) are also counted in a(n+1) and {n+1} is a subset counted in a(n+1) but not a(n), a(n + 1) > a(n) for n >= 1.
As every subset counted in a(n + 1) that contains n+1 can be found from some subset counted in a(n) by appending n+1 and every subset counted in a(n) not containing n + 1 is counted in a(n + 1), a(n+1) <= 2*a(n). (End)
FORMULA
a(n) < a(n + 1) <= 2 * a(n). - David A. Corneth, Aug 02 2023
EXAMPLE
The a(0) = 1 through a(5) = 18 subsets:
{} {} {} {} {} {}
{1} {1} {1} {1} {1}
{2} {2} {2} {2}
{3} {3} {3}
{1,3} {4} {4}
{2,3} {1,3} {5}
{1,4} {1,3}
{2,3} {1,4}
{3,4} {1,5}
{2,3,4} {2,3}
{2,5}
{3,4}
{3,5}
{4,5}
{1,3,5}
{2,3,4}
{3,4,5}
{2,3,4,5}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], Intersection[#, Differences[#]]=={}&]], {n, 0, 10}]
PROG
(Python)
from itertools import combinations
def A364463(n): return sum(1 for l in range(n+1) for c in combinations(range(1, n+1), l) if set(c).isdisjoint({c[i+1]-c[i] for i in range(l-1)})) # Chai Wah Wu, Sep 26 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 27 2023
EXTENSIONS
a(21)-a(29) from David A. Corneth, Aug 02 2023
a(30)-a(32) from Chai Wah Wu, Sep 26 2023
a(33)-a(35) from Chai Wah Wu, Sep 27 2023
STATUS
approved