

A195738


Triangle read by rows: DR(n,d) is the number of properly ddimensional polyominoes with n cells, modulo translations and rotations (n >= 1, 0 <= d <= n1).


12



1, 0, 1, 0, 1, 1, 0, 1, 6, 3, 0, 1, 17, 17, 4, 0, 1, 59, 131, 52, 7, 0, 1, 195, 915, 709, 153, 13, 0, 1, 703, 6553, 8946, 3350, 454, 28
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OFFSET

1,9


COMMENTS

Table 1 (p. 366) in Lunnon (1975) contains more terms. Because the table there (in the reference) has incomplete columns, the extra terms do not appear in this triangular sequence (array).
Entry DR(n=11, d=2) in Table 1 (p. 366) must be a typo. It should not be 33890, but 33895. This was corrected by N. J. A. Sloane in 2011 in the documentation of sequence A006758. (See also sequence A000988.)
(End)
The number of oriented polyominoes (chiral pairs counted as two) here is the sum of the number of unoriented polyominoes (chiral pairs counted as one) in A049430 and the number of chiral pairs.  Robert A. Russell, May 03 2020


LINKS



FORMULA

We can add unoriented and chiral pairs for the top two diagonals. The summands have quick algorithms. (End)


EXAMPLE

Triangle begins:
n\d 0 1 2 3 4 5 6 7
+=
1  1
2  0 1
3  0 1 1
4  0 1 6 3
5  0 1 17 17 4
6  0 1 59 131 52 7
7  0 1 195 915 709 153 13
8  0 1 703 6553 8946 3350 454 28
...


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



