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

0,3

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.

Links

Table of n, a(n) for n=0..36.

Rémy Sigrist, C++ program

Example

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.

Prog

(C++) // See Links section.

Crossrefs

Cf. A374664.

Sequence in context: A266384 A248825 A001641 * A007382 A127804 A027306

Adjacent sequences: A374709 A374710 A374711 * A374713 A374714 A374715

Keyword

nonn,base

Author

Rémy Sigrist, Jul 17 2024

Status

approved