A374712 a(n) is the number of binary strings of length n that have no common ones with some of their cyclic shifts.

1, 1, 3, 4, 11, 16, 30, 50, 115, 157, 338, 507, 1094, 1587, 3538, 4594, 11379, 14842, 33717, 44879, 108346, 129119, 328353, 401029, 990670, 1176391, 3021359, 3366733, 9202918, 10146579, 26569610, 29412429, 82152435, 83243894, 250231696, 288536609, 866141480

Offset: 0

Author

Rémy Sigrist, Jul 17 2024

Keywords

• nonn
• base

Comments

For n > 0, a(n) is the number of subsets S of Z_n such that S and S + t are disjoint for some t in Z_n.

Examples

			For n = 4: the following binary strings of length 4 have no common ones with some of their cyclic shifts: "0000", "0001", "0010", "0011", "0100", "0101", "0110", "1000", "1001", "1010" and "1100", so a(4) = 11.
		

Links

• Rémy Sigrist, C++ program

Crossrefs

Cf. A374664.