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

11, 90, 357, 996, 2255, 4446, 7945, 13192, 20691, 31010, 44781, 62700, 85527, 114086, 149265, 192016, 243355, 304362, 376181, 460020, 557151, 668910, 796697, 941976, 1106275, 1291186, 1498365, 1729532, 1986471, 2271030, 2585121, 2930720, 3309867, 3724666

Offset: 1

Author

Geoffrey Critzer, Nov 05 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002492 (3 nodes).

Programs

Mathematica

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

PARI

Vec(-x*(x^3+17*x^2+35*x+11)/(x-1)^5  + O(x^100)) \\ Colin Barker, Sep 22 2013

Formula

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

G.f.: -x*(x^3+17*x^2+35*x+11) / (x-1)^5. - Colin Barker, Sep 22 2013

Extensions

More terms from Colin Barker, Sep 22 2013

Added a(4) = 996 from Vincenzo Librandi, Sep 23 2013