A060581 Number of homeomorphically irreducible general graphs on 6 labeled node and with n edges.

1, 15, 81, 441, 2151, 9957, 43122, 174162, 666267, 2403987, 8183601, 26281065, 79660856, 228180456, 618992466, 1595081266, 3918506466, 9211519476, 20797923546, 45258309066, 95225448306, 194283668576, 385361919996

Offset

0,2

Comments

A homeomorphically irreducible general graph is a graph with multiple edges and loops and without nodes of degree 2.

References

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.

Links

Table of n, a(n) for n=0..22.

V. Jovovic, Generating functions for homeomorphically irreducible general graphs on n labeled nodes

V. Jovovic, Recurrences for the numbers of homeomorphically irreducible general graphs on m labeled nodes and n edges

Formula

G.f.: (6*x^30 - 30*x^29 - 90*x^28 + 898*x^27 - 5703*x^26 + 67854*x^25 - 552925*x^24 + 2795730*x^23 - 9663357*x^22 + 24476292*x^21 - 47540991*x^20 + 73129860*x^19 - 91373250*x^18 + 94675608*x^17 - 82549758*x^16 + 60794764*x^15 - 37293240*x^14 + 18277860*x^13 - 6426742*x^12 + 945252*x^11 + 680499*x^10 - 726250*x^9 + 423825*x^8 - 187536*x^7 + 66981*x^6 - 19092*x^5 + 4065*x^4 - 560*x^3 + 24*x^2 + 6*x - 1)/(x - 1)^21. E.g.f. for homeomorphically irreducible general graphs with n nodes and k edges is (1 + x*y)^( - 1/2)*exp( - x*y/2 + x^2*y^2/4)*Sum_{k >= 0} 1/(1 - x)^binomial(k + 1, 2)*exp( - x^2*y*k^2/(2*(1 + x*y)) - x^2*y*k/2)*y^k/k!.

Crossrefs

Cf. A003514, A060516, A060533-A060537, A060576-A060581.

Sequence in context: A309336 A266288 A213552 * A253222 A334244 A284900

Adjacent sequences: A060578 A060579 A060580 * A060582 A060583 A060584

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 03 2001

Status

approved