Sequences that pass recursion test, but ...

[Tanya Khovanova]

Sequential greetings,

Consider the set S of n curves node(i)=sin(i*t+k(i)),
where i is an integer from 1 to n.
Form the graph G by connecting the nodes of S that
have a common local maximal point.
How many different waveforms may the sum of the
elements of S have, so that G is a connected graph?
	The first few answers a(n) for n=1 to 6 are:
a(1)=1,
a(2)=1,
a(3)=4,
a(4)=26,
a(5)=926 and
a(6)=11622.
	I’ve only been able to count so far yet. Furthermore,
I’m not sure I haven’t  miscounted.
	Can someone please help finding a general term for
a(n), or, at least, extend a bit the list?

	Thank you for your attention.

Paulo Sachs

P.S. Excuse my annoying English, for I am not a native
writer. I hope I havent't done to many
incomprehensible mistakes.


		
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