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

1,1

Links

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A002492 (3 nodes).

Sequence in context: A155607 A356323 A110252 * A171470 A168585 A055425

Adjacent sequences: A199391 A199392 A199393 * A199395 A199396 A199397

Keyword

nonn,easy

Author

Geoffrey Critzer, Nov 05 2011

Extensions

More terms from Colin Barker, Sep 22 2013

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

Status

approved