A396986 The number of n-colorings of the vertices of the truncated cuboctahedron up to rotation.

0, 1, 11728130343936, 3323601794975613468921, 3301173438094452954283114496, 148029736616687561074943603515625, 935510737806439886780527739609465856, 1529307009053921893456435099183552091601, 929197716605442630899092482218600018477056

Offset

0,3

Comments

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

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

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Formula

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

Mathematica

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

Crossrefs

Cf. A378474 (rotation and reflection).

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).

Sequence in context: A250492 A095429 A261151 * A103575 A172551 A172615

Adjacent sequences: A396983 A396984 A396985 * A396987 A396988 A396989

Keyword

nonn,easy

Author

Peter Kagey, Jun 12 2026

Status

approved