[seqfan] Re: A005207+1 and A296516 as numbers of terms in some polynomials

[Brad Klee]

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