OFFSET
0,2
COMMENTS
A pair of positive integers is a binary containment if the positions of 1's in the reversed binary expansion of the first are a subset of the positions of 1's in the reversed binary expansion of the second.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..129, (terms up to a(71) from Alois P. Heinz)
FORMULA
a(2^n - 1) = A014466(n).
EXAMPLE
The a(0) = 1 through a(6) = 18 subsets:
{} {} {} {} {} {} {}
{1} {1} {1} {1} {1} {1}
{2} {2} {2} {2} {2}
{1,2} {3} {3} {3} {3}
{1,2} {4} {4} {4}
{1,2} {5} {5}
{1,4} {1,2} {6}
{2,4} {1,4} {1,2}
{3,4} {2,4} {1,4}
{1,2,4} {2,5} {1,6}
{3,4} {2,4}
{3,5} {2,5}
{1,2,4} {3,4}
{3,5}
{3,6}
{5,6}
{1,2,4}
{3,5,6}
MAPLE
c:= proc() option remember; local i, x, y;
x, y:= map(n-> Bits[Split](n), [args])[];
for i to nops(x) do
if x[i]=1 and y[i]=0 then return false fi
od; true
end:
b:= proc(n, s) option remember; `if`(n=0, 1, b(n-1, s)+
`if`(ormap(i-> c(n, i), s), 0, b(n-1, s union {n})))
end:
a:= n-> b(n, {}):
seq(a(n), n=0..34); # Alois P. Heinz, Mar 28 2019
MATHEMATICA
binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[Subsets[Range[n]], stableQ[#, SubsetQ[binpos[#1], binpos[#2]]&]&]], {n, 0, 13}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 28 2019
EXTENSIONS
a(16)-a(45) from Alois P. Heinz, Mar 28 2019
STATUS
approved