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A060533 Number of homeomorphically irreducible multigraphs (or series-reduced multigraphs or multigraphs without nodes of degree 2) on 3 labeled nodes. 11
1, 3, 0, 3, 9, 12, 19, 27, 36, 46, 57, 69, 82, 96, 111, 127, 144, 162, 181, 201, 222, 244, 267, 291, 316, 342, 369, 397, 426, 456, 487, 519, 552, 586, 621, 657, 694, 732, 771, 811, 852, 894, 937, 981, 1026, 1072, 1119, 1167, 1216, 1266, 1317, 1369, 1422 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Vladeta Jovovic, Generating functions for homeomorphically irreducible multigraphs on n labeled nodes

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: (3*x^7 - 7*x^6 + 6*x^5 + 3*x^4 - 11*x^3 + 6*x^2 - 1)/(x - 1)^3.

E.g.f. for homeomorphically irreducible multigraphs 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, 2)*exp( - x^2*y*k^2/(2*(1 + x*y)) - x^2*y*k/2)*y^k/k!.

From Colin Barker, Nov 10 2016: (Start)

a(n) = (1 + n)*(2 + n)/2 - 9 for n>4.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7. (End)

MATHEMATICA

i=5; s=1; lst={s}; Do[s+=n+i; If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 30 2008 *)

PROG

(PARI) Vec((3*x^7-7*x^6+6*x^5+3*x^4-11*x^3+6*x^2-1)/(x-1)^3 + O(x^60)) \\ Colin Barker, Nov 10 2016

CROSSREFS

Cf. A003514, A060516, A060534-A060537.

Sequence in context: A021333 A104141 A279977 * A177785 A212036 A191619

Adjacent sequences:  A060530 A060531 A060532 * A060534 A060535 A060536

KEYWORD

nonn,easy

AUTHOR

Vladeta Jovovic, Apr 01 2001

STATUS

approved

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Last modified February 24 00:19 EST 2020. Contains 332195 sequences. (Running on oeis4.)