A329128 Number of nonequivalent sets whose translations and reflections cover {1..n}.

1, 2, 3, 6, 8, 17, 24, 52, 77, 171, 265, 593, 952, 2131, 3519, 7846, 13238, 29351, 50374, 111031, 193155, 423403, 744616, 1624302, 2881784, 6260030, 11186219, 24213106, 43522800, 93922741, 169653109, 365172178

Offset: 1

Author

Andrew Howroyd, Nov 07 2019

Keywords

• nonn
• more

Comments

Equivalence is up to translation and reflection. Only translations and reflections that are subsets of {1..n} are included.

Examples

			For n = 4 there are 6 sets (up to equivalence) that with their reflections and translations cover {1..4}:
  {{1}, {2}, {3}, {4}};
  {{1, 2}, {2, 3}, {3, 4}};
  {{1, 3}, {2, 4}};
  {{1, 2, 4}, {1, 3, 4}};
  {{1, 2, 3}, {2, 3, 4}};
  {{1, 2, 3, 4}}.
.
For n = 5 there are 8 sets (up to equivalence) that with their reflections and translations cover {1..5}:
  {{1}, {2}, {3}, {4}, {5}};
  {{1, 2}, {2, 3}, {3, 4}, {4, 5}};
  {{1, 3}, {2, 4}, {3, 5}};
  {{1, 2, 4}, {1, 3, 4}, {2, 3, 5}, {2, 4, 5}};
  {{1, 2, 3}, {2, 3, 4}, {3, 4, 5}};
  {{1, 2, 3, 5}, {1, 3, 4, 5}};
  {{1, 2, 3, 4}, {2, 3, 4, 5}};
  {{1, 2, 3, 4, 5}}.
		

Crossrefs

Cf. A079500 (if only translations allowed).

Cf. A096202, A096203, A329235.