cp's OEIS Frontend

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

%I A096203 #16 Nov 08 2019 22:26:59
%S A096203 1,2,3,7,18,66,239,963,3792,15230,60297,240295,952530,3783000,
%T A096203 14999274,59492918,235852544,935260075,3707948564,14702345112,
%U A096203 58294850481,231152521791,916584704599,3634684693457,14413639272087
%N A096203 Number of coverings of {1..n} by translation and reflection of a single set.
%e A096203 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:
%e A096203   {{1}, {2}, {3}, {4}};
%e A096203   {{1, 2}, {3, 4}};
%e A096203   {{1, 2}, {2, 3}, {3, 4}};
%e A096203   {{1, 3}, {2, 4}};
%e A096203   {{1, 2, 4}, {1, 3, 4}};
%e A096203   {{1, 2, 3}, {2, 3, 4}};
%e A096203   {{1, 2, 3, 4}}.
%e A096203 .
%e A096203 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:
%e A096203   {{1}, {2}, {3}, {4}, {5}};
%e A096203   {{1, 2}, {2, 3}, {3, 4}, {4, 5}};
%e A096203   {{1, 2}, {2, 3}, {4, 5}};
%e A096203   {{1, 2}, {3, 4}, {4, 5}};
%e A096203   {{1, 3}, {2, 4}, {3, 5}};
%e A096203   {{1, 2, 4}, {1, 3, 4}, {2, 3, 5}, {2, 4, 5}};
%e A096203   {{1, 2, 4}, {1, 3, 4}, {2, 3, 5}};
%e A096203   {{1, 2, 4}, {1, 3, 4}, {2, 4, 5}};
%e A096203   {{1, 2, 4}, {2, 3, 5}, {2, 4, 5}};
%e A096203   {{1, 3, 4}, {2, 3, 5}, {2, 4, 5}};
%e A096203   {{1, 2, 3}, {2, 3, 4}, {3, 4, 5}};
%e A096203   {{1, 2, 4}, {2, 3, 5}};
%e A096203   {{1, 3, 4}, {2, 3, 5}};
%e A096203   {{1, 3, 4}, {2, 4, 5}};
%e A096203   {{1, 2, 3}, {3, 4, 5}};
%e A096203   {{1, 2, 3, 5}, {1, 3, 4, 5}};
%e A096203   {{1, 2, 3, 4}, {2, 3, 4, 5}};
%e A096203   {{1, 2, 3, 4, 5}}.
%Y A096203 Cf. A096202 (if only translations allowed).
%Y A096203 Cf. A096154, A329128.
%K A096203 nonn
%O A096203 1,2
%A A096203 _Jon Wild_, Jul 27 2004
%E A096203 Corrected by _Andrew Howroyd_, Nov 08 2019