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 A384782 #24 Jun 15 2025 14:36:56 %S A384782 1,1,1,0,1,1,0,3,4,2,0,3,18,12,7,0,6,60,126,75,23,0,3,165,751,1025, %T A384782 473,112,0,3,346,3784,9414,8936,3539,607,0,1,565,14112,66503,108739, %U A384782 80531,27027,3811,0,1,723,42420,362939,994542,1204093,725795,212122,25413,0,0,723,101237,1586479,7065791,13389295,12792264,6512671,1678783,178083 %N A384782 Triangle read by rows: T(n,k) is the number of face-connected polyhedral components consisting of k cuboctahedra and n-k octahedra in the rectified cubic honeycomb up to translation, rotation, and reflection of the honeycomb, 0<=k<=n. %C A384782 Also the number of face-connected polyhedral components consisting of k truncated cubes and n-k octahedra in the truncated cubic honeycomb up to translation, rotation, and reflection of the honeycomb. %C A384782 Row sums are given by A384254. %H A384782 Peter Kagey, <a href="/A384782/a384782.png">Illustration of row 4</a>. %H A384782 Wikipedia, <a href="https://en.wikipedia.org/wiki/Convex_uniform_honeycomb">Convex uniform honeycomb</a> %F A384782 T(n,n) = A038119(n). %e A384782 Table begins: %e A384782 0 | 1; %e A384782 1 | 1, 1; %e A384782 2 | 0, 1, 1; %e A384782 3 | 0, 3, 4, 2; %e A384782 4 | 0, 3, 18, 12, 7; %e A384782 5 | 0, 6, 60, 126, 75, 23; %e A384782 6 | 0, 3, 165, 751, 1025, 473, 112; %e A384782 7 | 0, 3, 346, 3784, 9414, 8936, 3539, 607; %e A384782 8 | 0, 1, 565, 14112, 66503, 108739, 80531, 27027, 3811; %e A384782 9 | 0, 1, 723, 42420, 362939, 994542, 1204093, 725795, 212122, 25413; %Y A384782 Cf. A384254. %Y A384782 Cf. A365970 (tetrahedral-octahedral honeycomb), A384486 (quarter cubic honeycomb), A384755 (omnitruncated cubic honeycomb). %K A384782 nonn,tabl %O A384782 0,8 %A A384782 _Peter Kagey_ and _Bert Dobbelaere_, Jun 09 2025