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

1,2

Links

Table of n, a(n) for n=1..25.

Example

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.

Sequence in context: A100388 A186232 A160181 * A328430 A143874 A073641

Adjacent sequences: A096200 A096201 A096202 * A096204 A096205 A096206

Keyword

nonn

Author

Jon Wild, Jul 27 2004

Extensions

Corrected by Andrew Howroyd, Nov 08 2019

Status

approved