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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. 12
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
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)
Sum_{n>=3} 1/a(n) = 1/72 + 2*tan(sqrt(73)*Pi/2)*Pi/sqrt(73). - Amiram Eldar, Jan 08 2023
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
Sequence in context: A348670 A104141 A279977 * A177785 A212036 A191619
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Apr 01 2001
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)