Generalization of Pell Sequence and Pell-Lucas Sequence, New Results and Circulant Matrices Aspects

Some generalizations of Pell sequence and Pell-Lucas sequence, namely, (k,h)-Pell sequence and (k,h)-Pell-Lucas sequence are considered in this paper. We obtain generating functions, some identities and formulas for the sums of a finite number of terms and consecutive terms, sums of squares of consecutive terms and alternating sums of consecutive terms of these sequences. Then, we obtain the eigenvalues and determinants of particular circulant matrices involving (k,h)-Pell sequence and (k,h)-Pell-Lucas sequence. Finally, we obtain some upper and lower bounds for the spectral norms of these circulant matrices.