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A049429 Triangle T(n,d) = number of distinct d-dimensional polyominoes (or polycubes) with n cells (0 < d < n).

%I A049429 #25 Aug 10 2022 22:36:01
%S A049429 1,1,1,1,4,2,1,11,11,3,1,34,77,35,6,1,107,499,412,104,11,1,368,3442,
%T A049429 4888,2009,319,23,1,1284,24128,57122,36585,8869,951,47,1,4654,173428,
%U A049429 667959,647680,231574,36988,2862,106,1,17072,1262464,7799183,11173880,5712765,1297366,146578,8516,235
%N A049429 Triangle T(n,d) = number of distinct d-dimensional polyominoes (or polycubes) with n cells (0 < d < n).
%C A049429 These are unoriented polyominoes of the regular tilings with Schläfli symbols {oo}, {4,4}, {4,3,4}, {4,3,3,4}, etc. Each tile is a regular orthotope (hypercube). For unoriented polyominoes, chiral pairs are counted as one. The dimension of the convex hull of the cell centers determines the dimension d. - _Robert A. Russell_, Aug 09 2022
%D A049429 Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.
%H A049429 R. C. Schroeppel, <a href="http://www.experimentalmath.info/workshop2004/schroeppel-talk.pdf">A few mathematical experiments</a>
%e A049429 From _Robert A. Russell_, Aug 09 2022: (Start)
%e A049429 Triangle begins with T(2,1):
%e A049429 n\d 1     2       3       4        5       6       7      8    9  10
%e A049429 2   1
%e A049429 3   1     1
%e A049429 4   1     4       2
%e A049429 5   1    11      11       3
%e A049429 6   1    34      77      35        6
%e A049429 7   1   107     499     412      104      11
%e A049429 8   1   368    3442    4888     2009     319      23
%e A049429 9   1  1284   24128   57122    36585    8869     951     47
%e A049429 10  1  4654  173428  667959   647680  231574   36988   2862  106
%e A049429 11  1 17072 1262464 7799183 11173880 5712765 1297366 146578 8516 235
%e A049429 (End)
%Y A049429 Cf. A049430 (col. d=0 added), A195738 (oriented), A195739 (fixed).
%Y A049429 Diagonals (with algorithms) are A000055, A036364, A355053.
%Y A049429 Row sums give A005519. Columns are A006765-A006768.
%K A049429 nonn,nice,tabl,hard
%O A049429 2,5
%A A049429 Richard C. Schroeppel
%E A049429 Two more rows added by _Robert A. Russell_, Aug 09 2022.