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We present a proof of a conjecture of Goh and Wildberger on the factorization of the spread polynomials. We indicate how the factors can be effectively calculated and exhibit a connection to the factorization of Fibonacci numbers into primitive parts., Comment: 8 pages

We obtain formulas for the coefficients of positive and negative powers of a partial theta function., Comment: 5 pages

We give a simplified presentation of some results about recurrences of certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials., Comment: 15 pages

Based on well-known properties of Fibonacci and Lucas numbers and polynomials we give a self-contained approach to some bivariate analogs., Comment: 21 pages

We consider Hankel determinants of the sequence of Catalan numbers modulo 2 (interpreted as integers 0 and 1) and more generally Hankel determinants where the sum over all permutations reduces to a single signed permutation., Comment: 34 pages

We give a survey of some known and some new results about factors of different sorts of $q-$Fibonacci numbers., Comment: Since I became aware of the fact that some of my experimentally found results have already been proved in a paper by H. Pan I changed the title and revised the paper thoroughly

Due to some results by John P. D Angelo and Dusty Grundmeier about CR- mappings the main results of my 2001 paper about recurrences for some sequences of binomial sums can be simplified., Comment: 13 pages

We study matrices which transform the sequence of Fibonacci or Lucas polynomials with even index to those with odd index and vice versa. They turn out to be intimately related to generalized Stirling numbers and to Bernoulli, Genocchi and tangent numbers and give rise to various identities between these numbers. There is also a close connection with the Akiyama-Tanigawa algorithm., Comment: 45 pages

We show that Genocchi and Bernoulli numbers are closely related to Fibonacci polynomials and derive some q-analogues.