A096203 Number of coverings of {1..n} by translation and reflection of a single set.

1, 2, 3, 7, 18, 66, 239, 963, 3792, 15230, 60297, 240295, 952530, 3783000, 14999274, 59492918, 235852544, 935260075, 3707948564, 14702345112, 58294850481, 231152521791, 916584704599, 3634684693457, 14413639272087

Offset: 1

Author

Jon Wild, Jul 27 2004

Keywords

• nonn

Examples

			a(4) = 7 because the following are the 7 coverings of {1...4}, each one of which only uses a single set and its translations and reflections:
  {{1}, {2}, {3}, {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}}.
.
a(5) = 18 because the following are the 18 coverings of {1...5}, each one of which only uses a single set and its translations and reflections:
  {{1}, {2}, {3}, {4}, {5}};
  {{1, 2}, {2, 3}, {3, 4}, {4, 5}};
  {{1, 2}, {2, 3}, {4, 5}};
  {{1, 2}, {3, 4}, {4, 5}};
  {{1, 3}, {2, 4}, {3, 5}};
  {{1, 2, 4}, {1, 3, 4}, {2, 3, 5}, {2, 4, 5}};
  {{1, 2, 4}, {1, 3, 4}, {2, 3, 5}};
  {{1, 2, 4}, {1, 3, 4}, {2, 4, 5}};
  {{1, 2, 4}, {2, 3, 5}, {2, 4, 5}};
  {{1, 3, 4}, {2, 3, 5}, {2, 4, 5}};
  {{1, 2, 3}, {2, 3, 4}, {3, 4, 5}};
  {{1, 2, 4}, {2, 3, 5}};
  {{1, 3, 4}, {2, 3, 5}};
  {{1, 3, 4}, {2, 4, 5}};
  {{1, 2, 3}, {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. A096202 (if only translations allowed).

Cf. A096154, A329128.

Extensions

Corrected by Andrew Howroyd, Nov 08 2019