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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). 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS From Petros Hadjicostas, Jan 11 2019: (Start) 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 Table of n, a(n) for n=1..36. W. F. Lunnon, Counting multidimensional polyominoes, Computer Journal 18 (4) (1975) 366-367. FORMULA From Robert A. Russell, May 03 2020: (Start) For n > 1, DR(n,n-1) = A000055(n) + A045649(n). DR(n,n-2) = A036364(n) + A036365(n). 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 Columns give A006758 (and A000988), A006759, A006760, A006761. Cf. A195739, A049430. Cf. A000055, A045649, A036364, A036365. Sequence in context: A351111 A154738 A355653 * A322632 A184082 A198868 Adjacent sequences: A195735 A195736 A195737 * A195739 A195740 A195741 KEYWORD nonn,tabl,more AUTHOR N. J. A. Sloane, Sep 22 2011 EXTENSIONS Sequence corrected by Petros Hadjicostas, Jan 11 2019 after observation by Jon E. Schoenfield STATUS approved

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Last modified September 9 22:43 EDT 2024. Contains 375765 sequences. (Running on oeis4.)