This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A355999 #10 Jul 27 2022 05:00:41
%S A355999 28,4240,344320,23872320,1603840000,109616815616,7785535242240,
%T A355999 580217967114240,45559682696478700,3774254616000000000,
%U A355999 329816052160897000000,30372942170151000000000,2943608844201080000000000
%N A355999 Number of fixed orthoplex n-ominoes with cell centers determining (n-3)-space.
%C A355999 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 A355999 a(n) = 2^(n-6) * n^(n-7) * (n-3) * (n-4) * (n-5) * (3n^3-17n^2+21n-78) / 3.
%F A355999 a(n) ~ A191092(n) / 4.
%e A355999 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.
%t A355999 Table[2^(n-6) n^(n-7) (n-3) (n-4) (n-5) (3n^3-17n^2+21n-78), {n,6,30}]
%o A355999 (Python)
%o A355999 def A355999(n): return int(((1<<n-6)*n**(n-7)*(n*(n*(n*(n*(n*(3*n - 53) + 366) - 1309) + 2943) - 4926) + 4680))//3) # _Chai Wah Wu_, Jul 26 2022
%Y A355999 Cf. A191092 (multidimensional), A355048 (unoriented), A355049 (chiral), A355051 (asymmetric).
%Y A355999 Diagonal 3 of A355997.
%K A355999 nonn
%O A355999 6,1
%A A355999 _Robert A. Russell_, Jul 22 2022