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A060534 Number of homeomorphically irreducible multigraphs (or series-reduced multigraphs or multigraphs without nodes of degree 2) on 4 labeled nodes. 2
1, 6, 3, 10, 48, 84, 182, 372, 699, 1222, 2007, 3132, 4688, 6780, 9528, 13068, 17553, 23154, 30061, 38484, 48654, 60824, 75270, 92292, 112215, 135390, 162195, 193036, 228348, 268596, 314276, 365916, 424077, 489354, 562377, 643812, 734362, 834768, 945810 (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 (6,-15,20,-15,6,-1).

FORMULA

G.f.: - (4*x^12 - 12*x^11 + 6*x^10 + 50*x^9 - 180*x^8 + 282*x^7 - 208*x^6 + 30*x^5 + 72*x^4 - 62*x^3 + 18*x^2 - 1)/((x - 1)^6).

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) = 60 + 48*(1+n) - 12*(1+n)*(2+n) + (1+n)*(2+n)*(3+n)*(4+n)*(5+n)/120 for n>6.

a(n) = 6*a(n-1)- 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>12.

(End)

PROG

(PARI) Vec(-(4*x^12-12*x^11+6*x^10+50*x^9-180*x^8+282*x^7-208*x^6+30*x^5+72*x^4-62*x^3+18*x^2-1)/((x-1)^6) + O(x^40)) \\ Colin Barker, Nov 10 2016

CROSSREFS

Cf. A003514, A060516, A060533, A060535-A060537.

Sequence in context: A066070 A272549 A112456 * A060445 A131894 A040033

Adjacent sequences:  A060531 A060532 A060533 * A060535 A060536 A060537

KEYWORD

nonn,easy

AUTHOR

Vladeta Jovovic, Apr 01 2001

STATUS

approved

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Last modified February 22 18:24 EST 2020. Contains 332148 sequences. (Running on oeis4.)