In this paper we will prove some generalized identities involving k-Fibonacci sequences and Fibonacci polynomials.

Test sequence generation is considered as an important phase of testing. Test sequences can be generated either by using code or model. Test sequence generation can be automated to make testing easier. This paper presents an approach for automatic test sequence generation from UML activity diagram of the Java7 Fork/Join framework. The activity diagram is first converted to an XML file, which is then traversed to find test sequences. Infeasible test sequences are avoided in this approach.Cost and overheads involved are also very less.

In this paper, we have introduced a new generalization of Jacobsthal polynomial (bi-periodic Jacobsthal polynomial), have obtained Binet’s formula, generating function, well-known Cassini’s, Catalan’s and d’Ocagne’s Identities and some more results related to this polynomial.

In this paper, we have obtained the infinite sum obtained from the reciprocals of Jacobsthal polynomial and Jacobsthal-Lucas polynomial. Also, we have obtained some inequalities involving the infinite sum of reciprocals of squares of Jacobsthal polynomial and Jacobsthal-Lucas polynomial.

In this paper, we will derive the explicit formulae for Chebyshev polynomials of the third and fourth kind with odd and even indices using the combinatorial method. Similar results are also deduced for their r-th derivatives. Finally, some identities involving Chebyshev polynomials of the third and fourth kind with even and odd indices and Fibonacci polynomials with negative indices are obtained.