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A199394 The number of ways to color the vertices of all (11) simple unlabeled graphs on 4 nodes using at most n colors. 1

%I #16 Sep 23 2013 09:54:11

%S 11,90,357,996,2255,4446,7945,13192,20691,31010,44781,62700,85527,

%T 114086,149265,192016,243355,304362,376181,460020,557151,668910,

%U 796697,941976,1106275,1291186,1498365,1729532,1986471,2271030,2585121,2930720,3309867,3724666

%N The number of ways to color the vertices of all (11) simple unlabeled graphs on 4 nodes using at most n colors.

%H Vincenzo Librandi, <a href="/A199394/b199394.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n)= 8*n^4/3 + 4*n^3 + 10*n^2/3 + n.

%F G.f.: -x*(x^3+17*x^2+35*x+11) / (x-1)^5. - _Colin Barker_, Sep 22 2013

%t Table[Total[Table[CycleIndex[GraphData[{4,k}, "Automorphisms"], s], {k, 1,11}] /. Table[s[i]-> n, {i, 1, 4}]], {n, 1, 25}]

%o (PARI) Vec(-x*(x^3+17*x^2+35*x+11)/(x-1)^5 + O(x^100)) \\ _Colin Barker_, Sep 22 2013

%Y Cf. A002492 (3 nodes).

%K nonn,easy

%O 1,1

%A _Geoffrey Critzer_, Nov 05 2011

%E More terms from _Colin Barker_, Sep 22 2013

%E Added a(4) = 996 from _Vincenzo Librandi_, Sep 23 2013

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Last modified February 28 08:11 EST 2024. Contains 370393 sequences. (Running on oeis4.)