[Fwd: SEQ+# A135929 FROM Artur Jasinski]

[Richard Mathar]

First off, why a(1)=0? It should be a(1)=1.

Second, this is duplicate of A010790:
http://www.research.att.com/~njas/sequences/A010790

It is generally a good idea to check for existing sequences before
submitting a new one.

Regards,
Max

On Dec 6, 2007 10:00 AM, Artur <grafix at csl.pl> wrote:
> I was contributed new sequence
>
> %I A135929
> %S A135929 0, 2, 12, 144, 2880
> %N A135929 Number of different Hamiltonian cycles in complete n vertices graph (also number of different roads in traveling salesman problem)
> %C A135929 A Hamiltonian cycle of a graph G is a cycle that visits every vertex in G exactly once, as opposed to an Eulerian cycle that visits each edge exactly once. K_n_n for n>1 are the only Hamiltonian complete bipartite graphs.
> %e A135929 a(3)=12 because different cycles in 3 Graph are
> {{1, 4, 2, 5, 3, 6, 1}, {1, 4, 2, 6, 3, 5, 1}, {1, 4, 3, 5, 2, 6, 1}, {1, 4, 3, 6, 2, 5, 1}, {1, 5, 2, 4, 3, 6, 1}, {1, 5, 2, 6, 3, 4, 1}, {1, 5, 3, 4, 2, 6, 1}, {1, 5, 3, 6, 2, 4, 1}, {1, 6, 2, 4, 3, 5, 1}, {1, 6, 2, 5, 3, 4, 1}, {1, 6, 3, 4, 2, 5, 1}, {1, 6, 3, 5, 2, 4, 1}}
> %t A135929 << DiscreteMath`Combinatorica`
> Table[a = Length[HamiltonianCycle[CompleteGraph[n, n], All]]; Print[a], {n, 1, 10}] (*Artur Jasinski*)
> %Y A135929 A061714, A001171
> %O A135929 1
> %K A135929 ,nonn,
> %A A135929 Artur Jasinski (grafix at csl.pl), Dec 06 2007
>
>
> ARTUR
>