A355997 -id:A355997 - cp's OEIS frontend

A355999 Number of fixed orthoplex n-ominoes with cell centers determining (n-3)-space.

28, 4240, 344320, 23872320, 1603840000, 109616815616, 7785535242240, 580217967114240, 45559682696478700, 3774254616000000000, 329816052160897000000, 30372942170151000000000, 2943608844201080000000000

Offset: 6

Robert A. Russell, Jul 22 2022

nonn

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.

			For a(6)=28, 6 of the 8 cubes in the 2^3 space are used. There are 12 cases where the 2 empty cubes share a face, 12 cases where they share an edge, and 4 cases where they share a vertex.

Cf. A191092 (multidimensional), A355048 (unoriented), A355049 (chiral), A355051 (asymmetric).

Diagonal 3 of A355997.

Table[2^(n-6) n^(n-7) (n-3) (n-4) (n-5) (3n^3-17n^2+21n-78), {n,6,30}]

def A355999(n): return int(((1<Chai Wah Wu, Jul 26 2022

a(n) = 2^(n-6) * n^(n-7) * (n-3) * (n-4) * (n-5) * (3n^3-17n^2+21n-78) / 3.

a(n) ~ A191092(n) / 4.

A355998 Number of fixed orthoplex n-ominoes with cell centers determining (n-2)-space.

Original entry on oeis.org

1, 48, 1728, 62720, 2457600, 105815808, 5017600000, 261227298816, 14860167413760, 918839084134400, 61439672177393700, 4421589120000000000, 340976534987475000000, 28064307240230900000000, 2456376885785930000000000

Offset: 4

Robert A. Russell, Jul 22 2022

nonn

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

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

Diagonal 2 of A355997.

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

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

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

cp's OEIS Frontend

A355999 Number of fixed orthoplex n-ominoes with cell centers determining (n-3)-space.

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