A249672 Number of simple labeled graphs of order n that have 3k connected components for some k.

1, 0, 0, 1, 6, 55, 826, 20839, 925470, 76332845, 12144225666, 3786386476697, 2323365229270526, 2810644438909846175, 6714880936575265290018, 31734660733696955320333111, 297106568811291486526250342118, 5516820501917771489801597101682245

Offset

0,5

Links

Table of n, a(n) for n=0..17.

Formula

E.g.f.: B(A(x) - 1) where B(x) is the e.g.f. for A079978 and A(x) is the e.g.f. for A001187.

Mathematica

nn = 18; a[x_] := Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}];
c[x_] := Log[a[x]];
Range[0, nn]! CoefficientList[
   Series[1/3 (E^x + 2 E^(-x/2) Cos[(Sqrt[3] x)/2]) /. x -> c[x], {x,
     0, nn}], x] // Simplify

Crossrefs

Cf. A218374, A218375.

Sequence in context: A095652 A132689 A323876 * A255853 A183594 A140790

Adjacent sequences: A249669 A249670 A249671 * A249673 A249674 A249675

Keyword

nonn

Author

Geoffrey Critzer, Nov 03 2014

Status

approved