A274902 - OEIS

%I #20 Sep 08 2022 08:46:17

%S 1,1432071648,3126973271816997,98382635718348789760,

%T 303164900659243306968750,214883849971608086273681376,

%U 55244392622152479810398651758,6760803201218467969357600653312,469341657186247418838800529901095,20833333333333465916666833583500000

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

%H Marko R. Riedel et al., <a href="http://math.stackexchange.com/questions/1854935/">Truncated objects coloring</a>, Mathematics Stack Exchange (Jul 10 2016).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Truncated_cube">Truncated cube</a>

%F 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.

%e 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.

%t 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 *)

%o (Magma) [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

%o +1/6*n^6: n in [1..20]]; // _Vincenzo Librandi_, Jul 11 2016

%Y Cf. A274900, A274901.

%K nonn,easy

%O 1,2

%A _Marko Riedel_, Jul 10 2016