This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A282816 #11 Feb 23 2017 04:32:52
%S A282816 0,0,1,11,76,340,1135,3101,7336,15576,30405,55495,95876,158236,251251,
%T A282816 385945,576080,838576,1193961,1666851,2286460,3087140,4108951,5398261,
%U A282816 7008376,9000200,11442925,14414751,18003636,22308076,27437915,33515185,40674976,49066336
%N A282816 Number of inequivalent ways to color the faces of a cube using at most n colors so that no two opposite sides have the same color.
%C A282816 Also the number of inequivalent ways to color the corners of an octahedron using at most n colors so that no two opposite corners have the same color.
%H A282816 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A282816 a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/24.
%F A282816 G.f.: -x^2*(1+4*x+20*x^2+4*x^3+x^4)/(x-1)^7 . - _R. J. Mathar_, Feb 23 2017
%e A282816 For n = 2 we get a(2) = 1 way to color the faces of a cube with two colors so that no two opposite sides have the same color.
%t A282816 Table[(8n(n-1) + n^3(n-1)^3) /24, {n, 0, 35}]
%o A282816 (PARI) a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/24 \\ _Charles R Greathouse IV_, Feb 22 2017
%Y A282816 Cf. A282817, A047780 (face colorings without restriction).
%K A282816 nonn,easy
%O A282816 0,4
%A A282816 _David Nacin_, Feb 21 2017