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%I #43 Oct 31 2023 12:06:02
%S 1,0,1,0,1,4,0,1,17,32,0,1,61,348,400,0,1,214,2836,8640,6912,0,1,758,
%T 21225,129288,254800,153664,0,1,2723,154741,1688424,6160640,8749056,
%U 4194304,0,1,9908,1123143,20762073,125055400,313921008,343901376,136048896
%N Triangle read by rows: DX(n,d) = number of properly d-dimensional polyominoes with n cells, modulo translations (n>=1, 0 <= d <= n-1).
%C According to Barequet-Barequet-Rote, p. 261, the value DX(7, 6) = 134209 given by W. F. Lunnon is incorrect; it should be 153664, see A127670. - _Alexander Knapp_, May 13 2013
%H Robert A. Russell, <a href="/A195739/b195739.txt">Table of n, a(n) for n = 1..60</a>
%H R. Barequet, G. Barequet, and G. Rote, <a href="http://page.mi.fu-berlin.de/rote/Papers/pdf/Formulae+and+growth+rates+of+high-dimensional+polycubes.pdf">Formulae and growth rates of high-dimensional polycubes</a>, Combinatorica 30 (2010), pp. 257-275.
%H W. F. Lunnon, <a href="http://dx.doi.org/10.1093/comjnl/18.4.366">Counting multidimensional polyominoes</a>, Computer Journal 18 (1975), no. 4, pp. 366-367.
%e Triangle begins with DX(1,0):
%e n\d 0 1 2 3 4 5 6
%e ---------------------------------------
%e 1...1
%e 2...0 1
%e 3...0 1 4
%e 4...0 1 17 32
%e 5...0 1 61 348 400
%e 6...0 1 214 2836 8640 6912
%e 7...0 1 758 21225 129288 254800 153664
%e ...
%Y Columns give A006762, A006763, A006764. Cf. A195738, A049430.
%Y Diagonals (with formulas) are A127670, A171860, A191092, A259015, A290738.
%K nonn,tabl
%O 1,6
%A _N. J. A. Sloane_, Sep 23 2011
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