A274900 Number of (not necessarily proper) vertex colorings of the truncated cube using at most n colors.

1, 352744, 5884691769, 5864100125056, 1241764261950625, 98716288267057896, 3991275742289356969, 98382635628154476544, 1661800900370941653561, 20833333346104183585000, 205202764127643987528241, 1656184316900213910466944, 11308349383297867766174569

Offset: 1

Author

Marko Riedel, Jul 10 2016

Keywords

• nonn
• easy

Comments

Also the number of vertex colorings of the rhombicuboctahedron up to rotation and reflection. - Peter Kagey, Nov 27 2024

Examples

			Cycle index: 1/48*s[1]^24 + 1/8*s[2]^10*s[1]^4 + 13/48*s[2]^12 + 1/6*s[3]^8 + 1/4*s[4]^6 + 1/6*s[6]^4.
		

Links

• Marko R. Riedel et al., Truncated objects coloring, Mathematics Stack Exchange (Jul 10 2016).
• Marko R. Riedel, Maple code for sequences A274900, A274901, A274902.
• Wikipedia, Truncated cube

Crossrefs

Cf. A274901, A274902.

Programs

Magma

[1/48*n^24+1/8*n^14+13/48*n^12+1/6*n^8+1/4*n^6+1/6*n^4: n in [1..20]]; // Vincenzo Librandi, Jul 11 2016

Mathematica

Table[1/48 n^24 + 1/8 n^14 + 13/48 n^12 + 1/6 n^8 + 1/4 n^6 + 1/6 n^4, {n, 25}] (* Vincenzo Librandi, Jul 11 2016 *)

PARI

a(n) = 1/48*n^24 + 1/8*n^14 + 13/48*n^12 + 1/6*n^8 + 1/4*n^6 + 1/6*n^4 \\ Felix Fröhlich, Jul 12 2016

Formula

a(n) = 1/48*n^24 + 1/8*n^14 + 13/48*n^12 + 1/6*n^8 + 1/4*n^6 + 1/6*n^4 = n^4*(n^20 + 6*n^10 + 13*n^8 + 8*n^4 + 12*n^2 + 8)/48.