Research Article

Incomplete $k$-Pell, $k$-Pell-Lucas and modified $k$-Pell numbers

Volume: 46 Number: 3 June 1, 2017
EN

Incomplete $k$-Pell, $k$-Pell-Lucas and modified $k$-Pell numbers

Abstract

In this paper, it is defined the incomplete $k$-Pell, $k$-Pell-Lucas and Modified $k$-Pell numbers, it is studied the recurrence relations, some properties of these sequences of integers and their generating functions.

Keywords

References

  1. Aires, A. P., Catarino, P., Campos, H., Borges, A. and Vasco, P. $s$-Generalized Fibonacci Numbers: Some Identities, a Generating Function and Pythagorean Triples, Int. J. Math. Anal. 8 (36), 1757-1766, 2014.
  2. Bolat, C. and Köse, H. On the Properties of $k$-Fibonacci Numbers, Int. J. Contemp. Math. Sci. 22 (5), 1097-1105, 2010.
  3. Catarino, P. On some identities for $k$-Fibonacci sequence, Int. J. Contemp. Math. Sci. 9 (1), 37-42, 2014.
  4. Catarino, P. A note involving Two-by-Two Matrices of the $k$-Pell and $k$-Pell-Lucas Se- quences, Int. Math. Forum 8 (32), 1561-1568, 2013.
  5. Catarino, P. On some identities and generating functions for $k$-Pell numbers, Int. J. Math. Anal. 7 (38), 1877-1884, 2013.
  6. Catarino, P. and Vasco, P. On Some Identities and Generating Functions for $k$-Pell-Lucas Sequence, Appl. Math. Sci. 7 (98), 4867-4873, 2013.
  7. Catarino, P. and Vasco, P. Modified $k$-Pell Sequence: Some Identities and Ordinary Gen- erating Function, Appl. Math. Sci. 7 (121), 6031-6037, 2013.
  8. Catarino, P., Vasco, P., Borges, A., Campos, H., and Aires, A. P. Sums, Products and identities involving $k$-Fibonacci and $k$-Lucas sequences, JP J. Algebra Number Theory Appl. 32 (1), 63-77, 2014.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Helena Campos This is me

Publication Date

June 1, 2017

Submission Date

October 20, 2015

Acceptance Date

April 11, 2016

Published in Issue

Year 2017 Volume: 46 Number: 3

APA
Catarino, P., & Campos, H. (2017). Incomplete $k$-Pell, $k$-Pell-Lucas and modified $k$-Pell numbers. Hacettepe Journal of Mathematics and Statistics, 46(3), 361-372. https://izlik.org/JA57LU93EN
AMA
1.Catarino P, Campos H. Incomplete $k$-Pell, $k$-Pell-Lucas and modified $k$-Pell numbers. Hacettepe Journal of Mathematics and Statistics. 2017;46(3):361-372. https://izlik.org/JA57LU93EN
Chicago
Catarino, Paula, and Helena Campos. 2017. “Incomplete $k$-Pell, $k$-Pell-Lucas and Modified $k$-Pell Numbers”. Hacettepe Journal of Mathematics and Statistics 46 (3): 361-72. https://izlik.org/JA57LU93EN.
EndNote
Catarino P, Campos H (June 1, 2017) Incomplete $k$-Pell, $k$-Pell-Lucas and modified $k$-Pell numbers. Hacettepe Journal of Mathematics and Statistics 46 3 361–372.
IEEE
[1]P. Catarino and H. Campos, “Incomplete $k$-Pell, $k$-Pell-Lucas and modified $k$-Pell numbers”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 3, pp. 361–372, June 2017, [Online]. Available: https://izlik.org/JA57LU93EN
ISNAD
Catarino, Paula - Campos, Helena. “Incomplete $k$-Pell, $k$-Pell-Lucas and Modified $k$-Pell Numbers”. Hacettepe Journal of Mathematics and Statistics 46/3 (June 1, 2017): 361-372. https://izlik.org/JA57LU93EN.
JAMA
1.Catarino P, Campos H. Incomplete $k$-Pell, $k$-Pell-Lucas and modified $k$-Pell numbers. Hacettepe Journal of Mathematics and Statistics. 2017;46:361–372.
MLA
Catarino, Paula, and Helena Campos. “Incomplete $k$-Pell, $k$-Pell-Lucas and Modified $k$-Pell Numbers”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 3, June 2017, pp. 361-72, https://izlik.org/JA57LU93EN.
Vancouver
1.Paula Catarino, Helena Campos. Incomplete $k$-Pell, $k$-Pell-Lucas and modified $k$-Pell numbers. Hacettepe Journal of Mathematics and Statistics [Internet]. 2017 Jun. 1;46(3):361-72. Available from: https://izlik.org/JA57LU93EN