A000719 Number of disconnected graphs with n nodes. (Formerly M1452 N0574)

0, 0, 1, 2, 5, 13, 44, 191, 1229, 13588, 288597, 12297299, 1031342116, 166123498733, 50668194387427, 29104827043066808, 31455591302381718651, 64032471448906164191208, 245999896712611657677614268, 1787823725136869060356731751124

Offset

0,4

Comments

a(n) is also the number of simple unlabeled graphs on n+1 nodes with diameter 2 and connectivity 1. - Geoffrey Critzer, Oct 23 2016

References

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..87 (first 31 terms from David Wasserman)

R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]

F. Harary, The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc. 78 (1955), 445-463.

M. L. Stein and P. R. Stein, Enumeration of Linear Graphs and Connected Linear Graphs up to p = 18 Points. Report LA-3775, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Oct 1967

Eric Weisstein's World of Mathematics, Disconnected Graph.

Eric Weisstein's World of Mathematics, k-Connected Graph.

Eric Weisstein's World of Mathematics, k-Edge-Connected Graph.

Mathematica

<< "Combinatorica`"; max = 18; A000088 = Table[ NumberOfGraphs[n], {n, 0, max}]; f[x_] = 1 - Product[ 1/(1 - x^k)^b[k], {k, 1, max}]; b[0] = b[1] = b[2] = 1; coes = CoefficientList[ Series[ f[x], {x, 0, max}], x]; sol = First[ Solve[ Thread[ Rest[ coes + A000088 ] == 0]]]; a[n_] := a[n] = A000088[[n+1]] - b[n] /. sol; a[0] = a[1] = 0; Table[a[n], {n, 0, max}] (* Jean-François Alcover, Nov 24 2011 *)

Crossrefs

Equals (A000088) minus (A001349).

Sequence in context: A212827 A212828 A212830 * A149875 A221546 A085632

Adjacent sequences: A000716 A000717 A000718 * A000720 A000721 A000722

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Christian G. Bower

Further terms from Vladeta Jovovic, Apr 14 2000

Status

approved