Yıl 2021,
Cilt: 34 Sayı: 4, 1089 - 1094, 01.12.2021
Anthony G. Shannon
,
Ömür Deveci
Kaynakça
- [1] Horadam, A.F., “Basic properties of a certain generalized sequence of numbers”, The Fibonacci Quarterly, 3: 161-176, (1965).
- [2] Deveci, O. and Shannon, A.G., “Pell-Padovan-circulant sequences and their applications”, Notes on Number Theory and Discrete Mathematics, 23 (3): 100-114, (2017).
- [3] Sloane, N.J.A., “The On-Line Encyclopedia of Integer Sequences”, http://oeis.org, (1964).
- [4] Hildebrand, F.B., Introduction to Numerical Analysis, McGraw-Hill, New York, p.461, (1956).
- [5] Feinberg, M., “New Slants”, The Fibonacci Quarterly, 2: 223-227, (1964).
- [6] Jarden, D., Recurring Sequences, Jerusalem: Riveon Lematika, p.114, (1966).
- [7] Shannon, A.G., Anderson, P.G. and Horadam, A.F., “Properties of Cordonnier, Perrin and Van der Laan numbers”, International Journal of Mathematical Education in Science and Technology, 37: 825-831, (2006).
- [8] Shannon, A.G., Horadam, A.F. and Anderson, P.G., “The auxiliary equation associated with the Plastic number”, Notes on Number Theory and Discrete Mathematics, 12: 1-12, (2006).
- [9] Shannon, A.G. and Wong, C.K., “Some Properties of Generalized Third Order Pell Numbers”, Congressus Numerantium, 201: 345-351, (2010).
- [10] Gnanadoss, A.A., “Contracting Bernoulli’s iteration and recurrence relations”, The Mathematical Gazette, 44: 221-223, (1960).
- [11] Anderson, P.G., Brown, T.C. and Shiue, P.J.-S., “A simple proof of a remarkable continued fraction identity”, Proceedings of the American Mathematical Society, 123:2005-2009, (1995).
- [12] Anderson, P.G., “Notes and extensions for a remarkable continued fraction”, The Fibonacci Quarterly, 55: 9-14, (2017).
- [13] Van der Cruyssen, P., “Linear difference equations and generalized continued fractions”, Computing, 22: 269-278, (1979).
- [14] Szekeres, G., “Multidimensional Continued Fractions”, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae Sectio Mathematica, 13: 113–140, (1970).
- [15] Van der Cruyssen. P., “A continued fraction algorithm”, Numerische Mathematik, 37: 149-156, ( 1981).
- [16] Bernstein, L., The Jacobi-Perron Algorithm: Its Theory and Application (Lecture Notes in Mathematics 207), Berlin: Springer, Ch.2, (1971).
Some Properties of a Third Order Partial Recurrence Relation
Yıl 2021,
Cilt: 34 Sayı: 4, 1089 - 1094, 01.12.2021
Anthony G. Shannon
,
Ömür Deveci
Öz
This paper explores a connection between third order recursive sequences and generalized continued fractions by analogy with second order recursive sequences and ordinary two-dimensional continued fractions. It does this with a partial recurrence relation which is related to the original third order recurrence relation, and raises a related conjecture.
Kaynakça
- [1] Horadam, A.F., “Basic properties of a certain generalized sequence of numbers”, The Fibonacci Quarterly, 3: 161-176, (1965).
- [2] Deveci, O. and Shannon, A.G., “Pell-Padovan-circulant sequences and their applications”, Notes on Number Theory and Discrete Mathematics, 23 (3): 100-114, (2017).
- [3] Sloane, N.J.A., “The On-Line Encyclopedia of Integer Sequences”, http://oeis.org, (1964).
- [4] Hildebrand, F.B., Introduction to Numerical Analysis, McGraw-Hill, New York, p.461, (1956).
- [5] Feinberg, M., “New Slants”, The Fibonacci Quarterly, 2: 223-227, (1964).
- [6] Jarden, D., Recurring Sequences, Jerusalem: Riveon Lematika, p.114, (1966).
- [7] Shannon, A.G., Anderson, P.G. and Horadam, A.F., “Properties of Cordonnier, Perrin and Van der Laan numbers”, International Journal of Mathematical Education in Science and Technology, 37: 825-831, (2006).
- [8] Shannon, A.G., Horadam, A.F. and Anderson, P.G., “The auxiliary equation associated with the Plastic number”, Notes on Number Theory and Discrete Mathematics, 12: 1-12, (2006).
- [9] Shannon, A.G. and Wong, C.K., “Some Properties of Generalized Third Order Pell Numbers”, Congressus Numerantium, 201: 345-351, (2010).
- [10] Gnanadoss, A.A., “Contracting Bernoulli’s iteration and recurrence relations”, The Mathematical Gazette, 44: 221-223, (1960).
- [11] Anderson, P.G., Brown, T.C. and Shiue, P.J.-S., “A simple proof of a remarkable continued fraction identity”, Proceedings of the American Mathematical Society, 123:2005-2009, (1995).
- [12] Anderson, P.G., “Notes and extensions for a remarkable continued fraction”, The Fibonacci Quarterly, 55: 9-14, (2017).
- [13] Van der Cruyssen, P., “Linear difference equations and generalized continued fractions”, Computing, 22: 269-278, (1979).
- [14] Szekeres, G., “Multidimensional Continued Fractions”, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae Sectio Mathematica, 13: 113–140, (1970).
- [15] Van der Cruyssen. P., “A continued fraction algorithm”, Numerische Mathematik, 37: 149-156, ( 1981).
- [16] Bernstein, L., The Jacobi-Perron Algorithm: Its Theory and Application (Lecture Notes in Mathematics 207), Berlin: Springer, Ch.2, (1971).