A050927 Number of directed multigraphs with loops on 3 nodes with n arcs.

1, 2, 10, 31, 90, 222, 520, 1090, 2180, 4090, 7356, 12660, 21105, 34020, 53460, 81891, 122826, 180510, 260746, 370370, 518518, 715870, 976170, 1315470, 1753975, 2314936, 3027224, 3923845, 5044920, 6436200, 8152542, 10255896

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,3,-5,-8,3,19,4,-24,-15,15,24,-4,-19,-3,8,5,-3,-2,1).

Formula

G.f.: (x^10+3*x^8+10*x^7+16*x^6+12*x^5+16*x^4+10*x^3+3*x^2+1) / ((1-x^3)^3*(1-x^2)^4*(1-x)^2).

Mathematica

<<Combinatorica`
nn=30; n=3; CoefficientList[Series[CycleIndex[Join[PairGroup[SymmetricGroup[n], Ordered], Permutations[Range[n*(n - 1) + 1, n*(n - 1) + n]], 2], s] /.Table[s[i] -> 1/(1 - x^i), {i, 1, n^2 - n}], {x, 0, nn}], x] (* Geoffrey Critzer, Aug 07 2015 *)
CoefficientList[Series[(x^10 + 3 x^8 + 10 x^7 + 16 x^6 + 12 x^5 + 16 x^4 + 10 x^3 + 3 x^2 + 1)/((1 - x^3)^3 (1 - x^2)^4 (1 - x)^2), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 08 2015 *)

Prog

(PARI) Vec((1 + 3*x^2 + 10*x^3 + 16*x^4 + 12*x^5 + 16*x^6 + 10*x^7 + 3*x^8 + x^10)/((1 - x)^2*(1 - x^2)^4*(1 - x^3)^3) + O(x^40)) \\ Andrew Howroyd, Mar 16 2020

Crossrefs

Column k=3 of A138107.

Cf. A005993.

Sequence in context: A193008 A024456 A197452 * A197302 A263782 A011921

Adjacent sequences: A050924 A050925 A050926 * A050928 A050929 A050930

Keyword

easy,nonn

Author

Vladeta Jovovic, Dec 30 1999

Status

approved