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Number of fixed orthoplex n-ominoes with cell centers determining (n-2)-space.
1

%I #6 Jul 26 2022 13:58:50

%S 1,48,1728,62720,2457600,105815808,5017600000,261227298816,

%T 14860167413760,918839084134400,61439672177393700,4421589120000000000,

%U 340976534987475000000,28064307240230900000000,2456376885785930000000000

%N Number of fixed orthoplex n-ominoes with cell centers determining (n-2)-space.

%C Orthoplex polyominoes are connected sets of cells of regular tilings with Schläfli symbols {}, {4}, {3,4}, {3,3,4}, {3,3,3,4}, etc. These are tilings of regular orthoplexes projected on their circumspheres. Orthoplex polyominoes are equivalent to multidimensional polyominoes that do not extend more than two units along any axis, i.e., fit within a 2^d cube. Two fixed polyominoes are identical only if one is a translation of the other.

%F a(n) = 2^(n-3) * n^(n-5) * (n-2) * (n-3)^2.

%F a(n) ~ A171860(n) / 2.

%e For A(4)=1, all 4 squares of the 2^2 space are used.

%t Table[2^(n-3) n^(n-5) (n-2) (n-3)^2, {n,4,30}]

%Y Cf. A171860 (multidimensional), A036367 (unoriented), A036368 (chiral), A036369 (asymmetric).

%Y Diagonal 2 of A355997.

%K nonn

%O 4,2

%A _Robert A. Russell_, Jul 22 2022