The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A261919 Number of n-node unlabeled graphs without isolated nodes or endpoints (i.e., no nodes of degree 0 or 1). 12
 1, 0, 0, 1, 3, 11, 62, 510, 7459, 197867, 9808968, 902893994, 153723380584, 48443158427276, 28363698856991892, 30996526139142442460, 63502034434187094606966, 244852545450108200518282934, 1783161611521019613186341526720, 24603891216946828886755056314074748 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES F. Harary, Graph Theory, Wiley, 1969. See illustrations in Appendix 1. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 (terms 1..26 from Max Alekseyev) N. J. A. Sloane, Illustration of a(0)-a(5) [Ignore the graphs with isolated nodes] FORMULA First differences of A004110: a(n) = A004110(n)-A004110(n-1). Euler transform of A004108, if we assume A004108(1) = 0. - Gus Wiseman, Aug 15 2019 EXAMPLE From Gus Wiseman, Aug 15 2019: (Start) Non-isomorphic representatives of the a(0) = 1 through a(5) = 11 graphs (empty columns not shown):   {}  {12,13,23}  {12,13,24,34}        {12,13,24,35,45}                   {13,14,23,24,34}     {12,14,25,34,35,45}                   {12,13,14,23,24,34}  {12,15,25,34,35,45}                                        {13,14,23,24,35,45}                                        {12,13,24,25,34,35,45}                                        {13,15,24,25,34,35,45}                                        {14,15,24,25,34,35,45}                                        {12,13,15,24,25,34,35,45}                                        {14,15,23,24,25,34,35,45}                                        {13,14,15,23,24,25,34,35,45}                                        {12,13,14,15,23,24,25,34,35,45} (End) MATHEMATICA permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m]; edges[v_] := Sum[GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total[Quotient[v, 2]]; b[n_] := Sum[permcount[p]*2^edges[p]*Coefficient[Product[1-x^p[[i]], {i, 1, Length[p]}], x, n-k]/k!, {k, 1, n}, {p, IntegerPartitions[k]}]; b[0] = 1; a[n_] := b[n] - b[n-1]; a /@ Range[0, 19] (* Jean-François Alcover, Sep 12 2019, after Andrew Howroyd in A004110 *) CROSSREFS Cf. A004108 (connected version), A004110 (version allowing isolated nodes). The labeled version is A100743. Cf. A003227, A006125, A007146, A059166, A095983, A322396. Sequence in context: A069725 A291287 A193499 * A232617 A326092 A292792 Adjacent sequences:  A261916 A261917 A261918 * A261920 A261921 A261922 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 15 2015 EXTENSIONS a(1)-a(11) computed by Brendan McKay, Sep 15 2015 a(12)-a(26) computed from A004110 by Max Alekseyev, Sep 16 2015 a(0) = 1 prepended by Gus Wiseman, Aug 15 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 19 19:30 EST 2020. Contains 332047 sequences. (Running on oeis4.)