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 A159233 #39 Feb 16 2025 08:33:10
%S A159233 0,0,0,0,49920,18936480,1293857280,34839270480,518880929280,
%T A159233 5122755187200,37376074229760,216261381584160,1041571537839360,
%U A159233 4323020652281760,15864787390932480,52496402135289840,159036030441200640,446469968164496640,1172916400659517440
%N A159233 Number of edge colorings of the Petersen graph.
%C A159233 The Petersen graph G is a cubic symmetric graph on 10 vertices and 15 edges with edge chromatic number 4. a(n) is also the number of (vertex) n-colorings of L(G), the line graph (or interchange graph) of G.
%C A159233 "An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring containing the smallest possible number of colors for a given graph is known as a minimum edge coloring." - Eric Weisstein, Edge Coloring.
%H A159233 Alois P. Heinz, <a href="/A159233/b159233.txt">Table of n, a(n) for n = 0..1000</a>
%H A159233 Timme, Marc; van Bussel, Frank; Fliegner, Denny; Stolzenberg, Sebastian (2009) "Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions", New J. Phys. 11 023001, doi: <a href="http://dx.doi.org/10.1088/1367-2630/11/2/023001">10.1088/1367-2630/11/2/023001</a>.
%H A159233 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PetersenGraph.html">Petersen Graph</a>
%H A159233 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeColoring.html">Edge Coloring</a>
%H A159233 Wikipedia, <a href="https://en.wikipedia.org/wiki/Edge_coloring">Edge Coloring</a>
%H A159233 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1).
%F A159233 a(n) = n^15 -30*n^14 + ... (see Maple program).
%F A159233 G.f.: 240 * x^4 * (120539*x^11 +4939568*x^10 +71258450*x^9 +441713760*x^8 +1285299570*x^7 +1834236432*x^6 +1296079344*x^5 +442507920*x^4 +68258235*x^3 +4153600*x^2 +75574*x +208) / (x-1)^16. - _Colin Barker_, Nov 28 2012
%p A159233 a:= n-> n^15 -30*n^14 +425*n^13 -3780*n^12 +23658*n^11 -110594*n^10 +399500*n^9 -1136005*n^8 +2560246*n^7 -4553907*n^6 +6285354*n^5 -6504300*n^4 +4739880*n^3 -2156064*n^2 +455616*n: seq(a(n), n=0..20);
%t A159233 Table[n^15 - 30 n^14 + 425 n^13 - 3780 n^12 + 23658 n^11 - 110594 n^10 + 399500 n^9 - 1136005 n^8 + 2560246 n^7 - 4553907 n^6 + 6285354 n^5 - 6504300 n^4 + 4739880 n^3 - 2156064 n^2 + 455616 n, {n, 0, 18}] (* _Michael De Vlieger_, Mar 27 2016 *)
%o A159233 (PARI) a(n)=prod(i=0,3,n-i)*(n^11 -24*n^10 +270*n^9 -1890*n^8 +9204*n^7 -32960*n^6 +89156*n^5 -183285*n^4 +282060*n^3 -310476*n^2 +220128*n -75936) \\ _Charles R Greathouse IV_, Nov 28 2012
%Y A159233 Cf. A270842 for edge colorings under the automorphisms of the Petersen graph. A296913.
%K A159233 nonn,easy
%O A159233 0,5
%A A159233 _Alois P. Heinz_, Apr 06 2009