A331462 Triangle read by rows: T(n,k) is the number of n X n binary matrices with k=0..n^2 ones forming a polyomino, under action of dihedral group of the square D_4.

0, 0, 1, 0, 1, 1, 1, 1, 0, 3, 2, 5, 6, 10, 8, 7, 3, 1, 0, 3, 4, 8, 17, 33, 68, 119, 195, 261, 300, 257, 169, 66, 20, 3, 1, 0, 6, 6, 16, 32, 82, 189, 470, 1076, 2422, 5010, 9732, 17145, 27399, 38680, 47560, 49325, 41872, 27864, 14095, 5280, 1470, 302, 48, 6, 1

Offset

0,10

Comments

By forming a polyomino it is meant that there is at least one 1 and that all the 1's are connected horizontally or vertically.

Links

Jean-Luc Manguin, Table of n, a(n) for n = 0..97

Jean-Luc Manguin, Illustration of a(3) and comparison with A268416

Example

Triangle begins:
  0;
  0, 1;
  0, 1, 1, 1, 1;
  0, 3, 2, 5, 6, 10, 8, 7, 3, 1;
  0, 3, 4, 8, 17, 33, 68, 119, 195, 261, 300, 257, 169, 66, 20, 3, 1;
  ...

Crossrefs

Cf. A054252, A268416.

Sequence in context: A194105 A194012 A255556 * A308410 A286111 A338209

Adjacent sequences: A331459 A331460 A331461 * A331463 A331464 A331465

Keyword

nonn,tabf

Author

Jean-Luc Manguin, Jan 17 2020

Status

approved