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International Journal of Mathematical Education in Science and Technology Volume 46, 2015 - Issue 8
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Classroom Notes

The odd-number sequence: squares and sums

J.V. LeyendekkersFaculty of Science, The University of Sydney, NSW 2006, Australia
&
A.G. ShannonFaculty of Engineering & IT, University of Technology, Sydney, NSW 2007, Australia;Registrar, Campion College, Old Toongabbie, NSW 2146, AustraliaCorrespondence[email protected]
Pages 1222-1228 | Received 04 Nov 2014, Published online: 02 Jun 2015

References

  • Leyendekkers JV, Shannon AG. Fibonacci and Lucas primes. Notes Number Theory Discrete Math. 2013;19(2):49–59.
  • Leyendekkers JV, Shannon AG. The Pascal-Fibonacci numbers. Notes Number Theory Discrete Math. 2013;19(3):49–59.
  • Leyendekkers JV, Shannon AG. The structural relationships between Fibonacci and prime-generated odd number sequences. Adv Stud Contemp Math. 2015;25(1):59–63.
  • Leyendekkers JV, Rybak JM. The generation and analyses of pythagorean triples within a 2-parameter Grid. Int J Math Educ Sci Technol. 1995;26(6):787–793.
  • Leyendekkers JV, Shannon AG, Rybak JM. Pattern recognition: modular rings and integer structure. North Sydney: Raffles KvB Monograph No.9; 2007.
  • Leyendekkers JV, Shannon AG. The number of primitive Pythagorean triples in a given interval. Notes Number Theory Discrete Math. 2012;18(1):49–57.
  • Shannon AG, Leyendekkers JV. Pythagorean Fibonacci patterns. Int J Mathemat Educ Sci Technol. 2012;43(4):554–559.
  • Shannon AG, Horadam AF. Arrowhead curves in a tree of Pythagorean triples. Int J Math Educ Sci Technol. 1994;25(2):255–261.
  • Hoggatt VE Jr. Fibonacci and Lucas numbers. Boston (MA): Houghton Mifflin; 1969, Equation (I11).
  • Leyendekkers JV, Rybak JM, Shannon AG. The characteristics of primes and other integers within the modular ring Z4 and in Class 1. Notes Number Theory Discrete Math. 1998;4(1):1–17.
  • Leyendekkers JV, Shannon AG. On sums of multiple squares. Notes Number Theory Discrete Math. 2012;18(1):9–15.
  • Watkins JJ. Number theory: a historical approach. Oxford: Princeton University Press; 2014.
  • Horadam AF, Shannon AG. Pell-type number generators of Pythagorean triples. In G.E. Bergum, A.N. Philippou, A.F. Horadam, editors. Applications of Fibonacci numbers. Vol. 5. Dordrecht: Kluwer; 1993, p. 331–343.
  • OEIS Foundation Inc. The on-line encyclopedia of integer sequences. 2014. Available from: http://oeis.org.

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