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Number of achiral multidimensional n-ominoes with cell centers determining n-3 space.
5

%I #12 Aug 09 2022 14:06:35

%S 1,5,23,115,668,3401,16469,74410,317612,1287147,5015932,18920467,

%T 69496943,249618639,879998839,3053446651,10452089459,35360685297,

%U 118416973230,393038044024,1294335897888,4232938101229,13757913332396

%N Number of achiral multidimensional n-ominoes with cell centers determining n-3 space.

%C Multidimensional polyominoes are connected sets of cells of regular tilings with Schläfli symbols {oo}, {4,4}, {4,3,4}, {4,3,3,4}, etc. Each tile is a regular orthotope (hypercube). This sequence is obtained using the first formula below. An achiral polyomino is identical to its reflection.

%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.

%F a(n) = A355053(n) - A355054(n) = 2*A355053(n) - A355052(n) = A355052(n) - 2*A355054(n).

%F a(n) = 2*A049430(n,n-3) - A195738(n,n-3), Lunnon's DE and DR arrays.

%e a(4)=1 as there is only one tetromino in one-space. a(5)=5 because there are 5 achiral pentominoes in 2-space, excluding the 1-D straight pentomino.

%Y Cf. A355052 (oriented), A355053 (unoriented), A355054 (chiral), A355056 (asymmetric), A191092 (fixed), A355050 (orthoplex), A195738 (Lunnon's DR), A049430 (Lunnon's DE).

%K nonn,easy

%O 4,2

%A _Robert A. Russell_, Jun 16 2022