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)
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
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Apr 01 2001
STATUS
approved