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A195738 Triangle read by rows: DR(n,d) is the number of properly d-dimensional polyominoes with n cells, modulo translations and rotations (n >= 1, 0 <= d <= n-1).

%I A195738 #55 May 13 2020 05:25:53
%S A195738 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,
%T A195738 13,0,1,703,6553,8946,3350,454,28
%N A195738 Triangle read by rows: DR(n,d) is the number of properly d-dimensional polyominoes with n cells, modulo translations and rotations (n >= 1, 0 <= d <= n-1).
%C A195738 From _Petros Hadjicostas_, Jan 11 2019: (Start)
%C A195738 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).
%C A195738 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.)
%C A195738 (End)
%C A195738 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
%H A195738 W. F. Lunnon, <a href="http://dx.doi.org/10.1093/comjnl/18.4.366">Counting multidimensional polyominoes</a>, Computer Journal 18 (4) (1975) 366-367.
%F A195738 From _Robert A. Russell_, May 03 2020: (Start)
%F A195738 For n > 1, DR(n,n-1) = A000055(n) + A045649(n).
%F A195738 DR(n,n-2) = A036364(n) + A036365(n).
%F A195738 We can add unoriented and chiral pairs for the top two diagonals. The summands have quick algorithms. (End)
%e A195738 Triangle begins:
%e A195738 n\d| 0    1    2    3    4    5    6    7
%e A195738 ---+---------------------------------=---
%e A195738 1  | 1
%e A195738 2  | 0    1
%e A195738 3  | 0    1    1
%e A195738 4  | 0    1    6    3
%e A195738 5  | 0    1   17   17    4
%e A195738 6  | 0    1   59  131   52    7
%e A195738 7  | 0    1  195  915  709  153   13
%e A195738 8  | 0    1  703 6553 8946 3350  454   28
%e A195738 ...
%Y A195738 Columns give A006758 (and A000988), A006759, A006760, A006761.
%Y A195738 Cf. A195739, A049430.
%Y A195738 Cf. A000055, A045649, A036364, A036365.
%K A195738 nonn,tabl,more
%O A195738 1,9
%A A195738 _N. J. A. Sloane_, Sep 22 2011
%E A195738 Sequence corrected by _Petros Hadjicostas_, Jan 11 2019 after observation by _Jon E. Schoenfield_