[Fwd: SEQ+# A135929 FROM Artur Jasinski]

[Max Alekseyev]

Oh, I see why it is a(1)=0.
But besides this first term, it is a duplicate of A010790, and I still
think that it does not deserve to be a separate sequence.

Max

On Dec 6, 2007 11:49 AM, Max Alekseyev <maxale at gmail.com> wrote:
> 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
> >
>



Martin said:
Another solution is n=19581212842 which has
n^2+n+1 = 3*7^2*13*19*31*37*43*61*79*97*103*4447

of a brute force search.  If 100 seqfans searched
for 100 days using ...  What IS the fastest program
for this sort of thing?  Mathematica, Pari, Sage?
Simon, what do you think?
(The question is, what is the smallest amicable 
number of the form n^2+n+1 ?)

Neil