A396986 - OEIS

%I #13 Jun 16 2026 10:11:58

%S 0,1,11728130343936,3323601794975613468921,

%T 3301173438094452954283114496,148029736616687561074943603515625,

%U 935510737806439886780527739609465856,1529307009053921893456435099183552091601,929197716605442630899092482218600018477056

%N The number of n-colorings of the vertices of the truncated cuboctahedron up to rotation.

%C Equivalently, the number of n-colorings of the faces of the disdyakis dodecahedron, which is the polyhedral dual of the truncated cuboctahedron.

%C Colorings are counted up to the rotational octahedral symmetry group of order 24.

%H Paolo Xausa, <a href="/A396986/b396986.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A378475(n^2).

%t A396986[n_] := n^12*(n^36 + 9*n^12 + 8*n^4 + 6)/24; Array[A396986, 10, 0] (* _Paolo Xausa_, Jun 16 2026 *)

%Y Cf. A378474 (rotation and reflection).

%Y Cf. A128766 (octahedron), A199406 (rhombic dodecahedron), A252704 (icosahedron), A252705 (dodecahedron), A274900 (rhombicuboctahedron), A274901 (truncated cube), A337963 (rhombic triacontahedron), A378473 (tetrakis hexahedron), A378475 (pentagonal icositetrahedron), A378476 (triakis icosahedron), A378477 (disdyakis triacontahedron), A378478 (pentagonal hexecontahedron), A378478 (pentagonal hexecontahedron), A395240 (bipyramids), A396861 (truncated icosahedron), A396913 (trapezohedron).

%K nonn,easy

%O 0,3

%A _Peter Kagey_, Jun 12 2026