A367123
Number of Hamiltonian cycles in the n-omino graph defined in A098891.
Original entry on oeis.org
1, 1, 0, 2, 16800
Offset: 1
For n = 4, there are a(4) = 2 Hamiltonian cycles in the tetromino graph: I-L-O-S-T-I and I-L-S-O-T-I, using conventional names of the tetrominoes.
For n = 5, one of the a(5) = 16800 Hamiltonian cycles in the pentomino graph is I-L-P-U-V-T-N-W-Z-F-X-Y-I.
See links for an example for n = 6.
A367440
Independence number of the polyomino graph PG(n) defined in A367435.
Original entry on oeis.org
1, 1, 1, 2, 4, 7, 18, 46
Offset: 1
A365621
Minimum size of a set of polyominoes with n cells such that all other free polyominoes with n cells can be obtained by moving one cell of one of the polyominoes in the set.
Original entry on oeis.org
1, 1, 1, 1, 2, 3, 7
Offset: 1
For n <= 3, any one polyomino with n cells is enough to construct the others (if any) by moving one cell, so a(n) = 1.
For n = 4, either the L or the T tetromino suffices to construct the other four, so a(4) = 1.
Below are examples of sets of a(n) polyominoes that are sufficient to construct all other polyominoes with n cells, 5 <= n <= 7:
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Showing 1-3 of 3 results.
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