%I #20 Sep 08 2022 08:46:17
%S 1,554,109152,5747200,128538250,1640929626,14167981324,91769978112,
%T 477063389475,2084653722250,7914860972876,26756396132544,
%U 82046630783572,231537699283450,608260629969000,1501341920229376,3508131297671589,7809071314434282,16646760371737000
%N Number of (not necessarily proper) face 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^14 + 1/8*n^10 + 1/16*n^9 + 1/16*n^8 + 7/48*n^7 + 1/6*n^6 + 1/8*n^5 + 1/8*n^4 + 1/6*n^3 = n^3*(n + 1)*(n^10 - n^9 + n^8 - n^7 + 7*n^6 - 4*n^5 + 7*n^4 + 8*n^2 - 2*n + 8)/48.
%e Cycle index: 1/48*s[1]^14 + 1/8*s[1]^6*s[2]^4 + 1/16*s[2]^5*s[1]^4 + 1/16*s[2]^6*s[1]^2 + 7/48*s[2]^7 + 1/6*s[1]^2*s[3]^4 + 1/8*s[4]^3*s[1]^2 + 1/8*s[4]^3*s[2] + 1/6*s[6]^2*s[2].
%t Table[1/48 n^14 + 1/8 n^10 + 1/16 n^9 + 1/16 n^8 + 7/48 n^7 + 1/6 n^6 + 1/8 n^5 + 1/8 n^4 + 1/6 n^3, {n, 25}] (* _Vincenzo Librandi_, Jul 11 2016 *)
%o (Magma) [1/48*n^14+1/8*n^10+1/16*n^9+1/16*n^8+7/48*n^7+1/6*n^6+1/8*n^5+ 1/8*n^4+1/6*n^3: n in [1..20]]; // _Vincenzo Librandi_, Jul 11 2016
%Y Cf. A274900, A274902.
%K nonn,easy
%O 1,2
%A _Marko Riedel_, Jul 10 2016