A201883 - OEIS

A201883

The number of simple labeled graphs on n nodes such that i) all connected components have exactly one cycle, ii) all vertices have degree at most 3, iii) vertices of degree 3 are on a cycle.

%I #27 May 26 2016 12:07:40

%S 1,0,0,1,15,192,2530,36165,570507,9969400,192525084,4087525095,

%T 94813475185,2387594185944,64886220442290,1892895183489583,

%U 58997625514583385,1956486468000839280,68781080882461076488,2555098360335768584385,100009432504671913008351

%N The number of simple labeled graphs on n nodes such that i) all connected components have exactly one cycle, ii) all vertices have degree at most 3, iii) vertices of degree 3 are on a cycle.

%F E.g.f.: ((1-x)/(1-2x))^(1/2)*exp((x^2-2x)/(4(1-x)^2)).

%F a(n) ~ (2*n)^n/exp(n+3/4). - _Vaclav Kotesovec_, Sep 24 2013

%F From _Benedict W. J. Irwin_, May 25 2016: (Start)

%F Let y(0)=1, y(1)=0, y(2)=0, y(3)=1/6,

%F Let 4ny(n)-(14n+15)y(n+1)+(18n+36)y(n+2)-(10n+30)y(n+3)+(2n+8)y(n+4)=0,

%F a(n) = n!*y(n).

%F (End)

%t a = x/(1 - x); Range[0, 20]! CoefficientList[Series[Exp[Log[1/(1 - a)]/2 - a/2 - a^2/4], {x, 0, 20}], x]

%K nonn

%O 0,5

%A _Geoffrey Critzer_, Dec 06 2011