login
A325096
Number of maximal subsets of {1...n} with no binary carries.
17
1, 1, 1, 2, 2, 3, 4, 5, 5, 7, 9, 10, 12, 13, 14, 15, 15, 20, 25, 27, 32, 34, 36, 37, 42, 44, 46, 47, 49, 50, 51, 52, 52, 67, 82, 87, 102, 107, 112, 114, 129, 134, 139, 141, 146, 148, 150, 151, 166, 171, 176, 178, 183, 185, 187, 188, 193, 195, 197, 198, 200, 201
OFFSET
0,4
COMMENTS
A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
LINKS
FORMULA
a(2^n - 1) = A000110(n).
EXAMPLE
The a(1) = 1 through a(9) = 7 maximal subsets:
{1} {12} {3} {34} {25} {16} {7} {78} {69}
{12} {124} {34} {25} {16} {168} {78}
{124} {34} {25} {258} {168}
{124} {34} {348} {249}
{124} {1248} {258}
{348}
{1248}
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}];
maxim[s_]:=Complement[s, Last/@Select[Tuples[s, 2], UnsameQ@@#&&SubsetQ@@#&]];
Table[Length[maxim[Select[Subsets[Range[n]], stableQ[#, Intersection[binpos[#1], binpos[#2]]!={}&]&]]], {n, 0, 10}]
KEYWORD
nonn,look
AUTHOR
Gus Wiseman, Mar 27 2019
EXTENSIONS
a(15)-a(61) from Alois P. Heinz, Mar 28 2019
STATUS
approved