Binomial transforms and applications of quadra fibona-pell sequences

In this study, first of all, the process of some special integer sequences and quaternions until today was examined. In the second part, basic information about special integer sequence, binomial coefficients, generating function and quaternions are given. In the third part, the binomial transform is defined for the quadra Fibona-Pell sequence, which is the main subject of thesis, and then the recurrence relation is found for this new binomial transform. Then the Binet formula of the sequence, the generating function and various sum formulas are found. In the fourth part, binomial transform is applied for the quadra Fibona-Pell quaternion, which was discussed in a thesis before. Next, similar results in the third section were found for binomial transform of the quadra Fibona-Pell quaternion. In the last part, results and suggestions are presented.