MJIS

Binet–Type Formula For The Sequence of Tetranacci Numbers by Alternate Methods

Gautams. Hathiwala and Devbhadra V. Shah

KEYWORDS

Binet formula, Fibonacci sequence, Tetranacci sequence.

PUBLISHED DATE September 2017
PUBLISHER Chitkara University
ABSTRACT

\"\\"\\\\"\\\\"\\"\"

Page(s)
URL http://dspace.chitkara.edu.in/jspui/bitstream/123456789/687/3/MJIS004_Hathiwala.pdf
ISSN 2278-957X
DOI 10.15415/mjis.2017.61004
REFERENCES
  • Arfken, G.: Diagonalization of Matrices, Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, 1985, 217–229.
  • Dresden G.P.B., Du Z.: A Simplified Binet Formula for Generalized Fibonacci Numbers, Journal of Integer Functions, Vol. 17, article 14.4.7, 2014.
  • Eigen decomposition of a matrix: http://mathworld.wolfram.com/EigenDecompositionTheorem.html
  • Hathiwala G. S., Shah D. V.: Golden proportions for the generalized Tetranacci numbers, International Research Journal of Mathematics, Enigneering and IT, Vol. 3, Issue 4, April 2016, 90–101.
  • Hathiwala G. S., Shah D. V.: “Periodicity of Tetranacci Numbers Modulo ”, The Journal of the Indian Academy of Mathematics, Vol. 38, Issue 2, 2016, pp. 155–165, ISSN: 0970 – 5120.
  • Lee G. Y., Lee G. S., Kim J. S., Shin H. K.: The Binet Formula and Representations of Generalized Fibonacci Numbers, Fibonacci Quarterly, Vol. 39, No. 2, May 2001, 158–164.
  • Mehta D. A.: Ph.D. thesis entitled “Properties of the Sequences of Tribonacci Numbers and Generalized Cut – off Numbers”, Veer Narmad South Gujarat University, Surat, India, Oct. 2009.
  • Raab J.A.: A Generalization of the Connection between the Fibonacci Sequence and Pascal’s Triangle, The Fibonacci Quarterly, Vol. 1, No. 3, Oct. 1963, 21–32.
  • Singh B., Bhatnagar S., Sikhwal O.: Fibonacci – Like Sequence, International Journal of Advanced Mathematical Sciences, Vol. 1, No. 3, 2013, 145–151.
  • Waddill M.E.: Some Properties of Tetranacci Numbers modulo , The Fibonacci Quarterly, Vol. 30, No. 3, Aug. 1992, 232–238.
  • Waddill M.E.: The Tetranacci Sequence and Generalizations, The Fibonacci Quarterly, Vol. 30, No. 1, Feb. 1992, 9–20.
  • Wall D. D.: Fibonacci Series Modulo , American Math. Monthly, Vol. 67, 1960, 525–532.