[seqfan] Re: A005207+1 and A296516 as numbers of terms in some polynomials
Brad Klee
bradklee at gmail.com
Sat Apr 14 17:19:44 CEST 2018
After: http://list.seqfan.eu/pipermail/seqfan/2018-April/018610.html
This is a nice iteration you have, where it's easy enough to prove that
MaxDeg( Q_{n} ) = MaxDeg( P_{n+1} ) = F(n+2) ,
especially by introducing notation ( Q_{F(n+2)} , P_{F(n+1)} ).
The algebra is not graded but bounded, implying F(n)^2 growth.
A maximum possible count of monomials for n>1 is
a(n) = (1/2)*F(n)*( 3 + F(n) ) = 2, 5, 9, 20, 44, 104, 252, 629 . . . (NAN)
This would be nice information to incorporate to your entry.
However, the picture already shows bounding by F(n)^2 ( cf. A007598 ).
Perhaps you can find a geometric approach involving lattice polygons ?
Cheers,
Brad
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