Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}

Kaynakça (15)

1. Carlitz, L. Generating function for powers of a certain sequences of numbers, Duke Math. J. 29, 521–537, 1962
2. Dujella, A. A bijective proof of Riordan’s theorem on powers of Fibonacci numbers, Discrete Math. 199, 217–220, 1999
3. Golomb, S.W. Problem 4720, Amer. Math. Monthly 64, 49, 1957
4. Hoggatt Jr., V.E. Fibonacci numbers and generalized binomial coefficients, The Fibonacci Quarterly 5, 383–400, 1967
5. Horadam, A.F. Generating functions for powers of a certain generalized sequence of num- bers, Duke Math. J. 32, 437–446, 1965
6. Kılıç, E. and Stanica, P. Factorizations and representations of second linear recurrences with indices in arithmetic progressions, Bol. Mex. Math. Soc. 15 (1), 23–36, 2009
7. Kılıç, E. and Stanica, P. Factorizations and representations of binary polynomial recurrences by matrix methods, Rocky Mount. J. Math., in press
8. Riordan, J. Generating functions for powers of Fibonacci numbers, Duke Math. J. 29, 5–12, 1962
9. Riordan, J. Combinatorial Identities (J. Wiley, New York, 1968)
10. Riordan, J. Inverse relations and combinatorial identities, Amer. Math. Monthly 71 (5), 485–498, 1964
11. Seibert, J. and Trojovsky, P. On sums of certain products of Lucas numbers, The Fibonacci Quarterly 44, 172–180, 2006
12. Seibert, J and Trojovsky, P. On multiple sums of products of Lucas numbers, J. Integer Seq. 10, 1–17, 2007
13. Shannon, A.G. A Method of Carlitz applied to the kth power generating function for Fi- bonacci numbers, The Fibonacci Quarterly 12, 293–299, 1974
14. Stanica, P. Generating function, weighted and non-weighted sums for powers of second-order recurrence sequences, The Fibonacci Quarterly 41 (4), 321–333, 2003
15. Vajda, S. Fibonacci and Lucas numbers and the Golden Section (Halsted Press, Brisbane, 1989).