The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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