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A096203
Number of coverings of {1..n} by translation and reflection of a single set.
3
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
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).
Sequence in context: A100388 A186232 A160181 * A328430 A143874 A073641
KEYWORD
nonn
AUTHOR
Jon Wild, Jul 27 2004
EXTENSIONS
Corrected by Andrew Howroyd, Nov 08 2019
STATUS
approved