cp's OEIS Frontend

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.

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.

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%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