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A355998
Number of fixed orthoplex n-ominoes with cell centers determining (n-2)-space.
1
1, 48, 1728, 62720, 2457600, 105815808, 5017600000, 261227298816, 14860167413760, 918839084134400, 61439672177393700, 4421589120000000000, 340976534987475000000, 28064307240230900000000, 2456376885785930000000000
OFFSET
4,2
COMMENTS
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.
FORMULA
a(n) = 2^(n-3) * n^(n-5) * (n-2) * (n-3)^2.
a(n) ~ A171860(n) / 2.
EXAMPLE
For A(4)=1, all 4 squares of the 2^2 space are used.
MATHEMATICA
Table[2^(n-3) n^(n-5) (n-2) (n-3)^2, {n, 4, 30}]
CROSSREFS
Cf. A171860 (multidimensional), A036367 (unoriented), A036368 (chiral), A036369 (asymmetric).
Diagonal 2 of A355997.
Sequence in context: A076003 A008845 A273627 * A288455 A371193 A231450
KEYWORD
nonn
AUTHOR
Robert A. Russell, Jul 22 2022
STATUS
approved