This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060577 #31 Jul 02 2025 16:02:01
%S A060577 1,1,4,6,11,17,24,32,41,51,62,74,87,101,116,132,149,167,186,206,227,
%T A060577 249,272,296,321,347,374,402,431,461,492,524,557,591,626,662,699,737,
%U A060577 776,816,857,899,942,986,1031,1077,1124,1172,1221,1271,1322,1374,1427
%N A060577 Number of homeomorphically irreducible general graphs on 2 labeled nodes and with n edges.
%C A060577 A homeomorphically irreducible general graph is a graph with multiple edges and loops and without nodes of degree 2.
%D A060577 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
%H A060577 V. Jovovic, <a href="/A060576/a060576.pdf">Generating functions for homeomorphically irreducible general graphs on n labeled nodes</a>
%H A060577 V. Jovovic, <a href="/A060576/a060576_rec.pdf">Recurrences for the numbers of homeomorphically irreducible general graphs on m labeled nodes and n edges</a>
%H A060577 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A060577 G.f.: (2*x^5 - 4*x^4 + 4*x^3 - 4*x^2 + 2*x - 1)/(x - 1)^3.
%F A060577 E.g.f. for homeomorphically irreducible general graphs 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 + 1, 2)*exp( - x^2*y*k^2/(2*(1 + x*y)) - x^2*y*k/2)*y^k/k!.
%F A060577 From _Marco Ripà_, Aug 20 2015: (Start)
%F A060577 a(n) = ceiling( (1/2)*(3*n^2 - 10*n + 9)/(n - 2) ) + floor( (3/2)*(n-1)^2 ) - n^2 + 3*n - 3 with n > 2, a(0) = a(1) = 1, a(2) = 4.
%F A060577 a(n) = n*(n + 3)/2 - 3 for n > 2.
%F A060577 a(n) = A046691(n-1) for n > 2. (End)
%p A060577 gf := (2*x^5 - 4*x^4 + 4*x^3 - 4*x^2 + 2*x - 1)/(x - 1)^3: s := series(gf, x, 100): for i from 0 to 100 do printf(`%d,`,coeff(s,x,i)) od:
%t A060577 Join[{1, 1, 4}, Table[n (n + 3)/2 - 3, {n, 3, 60}]] (* _Bruno Berselli_, Aug 20 2015 *)
%Y A060577 Cf. A003514, A046691, A060516, A060533-A060537, A060576-A060581.
%K A060577 nonn,easy
%O A060577 0,3
%A A060577 _Vladeta Jovovic_, Apr 04 2001
%E A060577 More terms from _James Sellers_, Apr 04 2001