A274901 -id:A274901 - cp's OEIS frontend

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

Marko Riedel, Jul 10 2016

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

			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.

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

Cf. A274901, A274902.

[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

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 *)

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

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.

A274902 Number of (not necessarily proper) edge colorings of the truncated cube using at most n colors.

Original entry on oeis.org

1, 1432071648, 3126973271816997, 98382635718348789760, 303164900659243306968750, 214883849971608086273681376, 55244392622152479810398651758, 6760803201218467969357600653312, 469341657186247418838800529901095, 20833333333333465916666833583500000

Offset: 1

Marko Riedel, Jul 10 2016

			Cycle index: 1/48*s[1]^36 + 1/8*s[2]^15*s[1]^6 + 1/16*s[2]^16*s[1]^4 + 1/8*s[2]^17*s[1]^2 + 1/12*s[2]^18 + 1/6*s[3]^12 + 1/4*s[4]^9 + 1/6*s[6]^6.

Marko R. Riedel et al., Truncated objects coloring, Mathematics Stack Exchange (Jul 10 2016).
Wikipedia, Truncated cube

Cf. A274900, A274901.

[1/48*n^36+1/8*n^21+1/16*n^20+1/8*n^19+1/12*n^18+1/6*n^12+1/4*n^9
+1/6*n^6: n in [1..20]]; // Vincenzo Librandi, Jul 11 2016

Table[1/48 n^36 + 1/8 n^21 + 1/16 n^20 + 1/8 n^19 + 1/12 n^18 + 1/6 n^12 + 1/4 n^9 + 1/6 n^6, {n, 25}] (* Vincenzo Librandi, Jul 11 2016 *)

a(n) = 1/48*n^36 + 1/8*n^21 + 1/16*n^20 + 1/8*n^19 + 1/12*n^18 + 1/6*n^12 + 1/4*n^9 + 1/6*n^6 = n^6*(n + 1)*(n^29 - n^28 + n^27 - n^26 + n^25 - n^24 + n^23 - n^22 + n^21 - n^20 + n^19 - n^18 + n^17 - n^16 + n^15 + 5*n^14 - 2*n^13 + 8*n^12 - 4*n^11 + 4*n^10 - 4*n^9 + 4*n^8 - 4*n^7 + 4*n^6 + 4*n^5 - 4 n^4 + 4*n^3 + 8*n^2 - 8*n + 8)/48.

cp's OEIS Frontend

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

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