A329235 Number of nonequivalent symmetric sets whose translations cover {1..n}.

1, 2, 3, 5, 6, 10, 12, 19, 23, 36, 44, 68, 84, 128, 161, 243, 308, 462, 592, 882, 1140, 1690, 2200, 3249, 4255, 6264, 8246, 12110, 16008, 23466, 31128, 45566, 60618, 88644, 118205, 172731, 230782, 337072, 451082, 658628, 882582, 1288432, 1728484, 2523104, 3388084

Offset

1,2

Comments

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

Symmetric sets are those such that the set remains unchanged after mapping each element x to m - x, where m is the sum of the greatest and least elements. All sets of at most two elements are symmetric.

Links

Table of n, a(n) for n=1..45.

Example

For n = 6 there are 10 symmetric sets (up to equivalence) that with their translations cover {1..6}:
  {{1}, {2}, {3}, {4}, {5}, {6}};
  {{1, 4}, {2, 5}, {3, 6}};
  {{1, 3}, {2, 4}, {3, 5}, {4, 6}};
  {{1, 3, 5}, {2, 4, 6}};
  {{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}};
  {{1, 2, 4, 5}, {2, 3, 5, 6}};
  {{1, 2, 3}, {2, 3, 4}, {3, 4, 5}, {4, 5, 6}};
  {{1, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 6}};
  {{1, 2, 3, 4, 5}, {2, 3, 4, 5, 6}};
  {{1, 2, 3, 4, 5, 6}}.

Crossrefs

Cf. A079500 (if symmetry is not required).

Cf. A096202, A329128.

Sequence in context: A212253 A237831 A347443 * A241829 A339511 A250179

Adjacent sequences: A329232 A329233 A329234 * A329236 A329237 A329238

Keyword

nonn

Author

Andrew Howroyd, Nov 08 2019

Status

approved