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How the odd terms in the Fibonacci sequence stack up

Published online by Cambridge University Press:  01 August 2016

S. Rinaldi  and
D. G. Rogers
S. Rinaldi
Affiliation:
Dipartimento di Scienze Matematiche ed Informatiche “R.Magari”, Università di Siena, Pian dei Mantellini 44, 53100 Siena, Italy email: rinaldi@unisi.it
D. G. Rogers
Affiliation:
Dipartimento di Scienze Matematiche ed Informatiche “R.Magari”, Università di Siena, Pian dei Mantellini 44, 53100 Siena, Italy email: rinaldi@unisi.it
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Extract

Dedicated to H. N. V. Temperley on the occasion of his ninetieth birthday 4 March 2005

The authors of the recent Note [1] exhibit an odd preference. They derive recurrence relations for the odd terms, un = F2n+1, n ≥ 0, in the sequence of Fibonacci numbers, Fn, defined by

Type
Articles
Information
The Mathematical Gazette , Volume 90 , Issue 519 , November 2006 , pp. 431 - 442
Copyright
Copyright © The Mathematical Association 2006

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References

1. Rajesh, V. and Leversha, G., Note 88.02: Some properties of odd terms of the Fibonacci sequence, Math. Gaz. 88 (March 2004) pp. 85–86.Google Scholar
2. Maynard, P., Feedback: Note 88.02, Math. Gaz. 88 (November 2004) p. 581.Google Scholar
3. Cross, T., Student Problem 2001.3, Math. Gaz. 85 (November 2001) pp. 527–528.Google Scholar
4. Benjamin, A.T. and Quinn, J.J., Proofs that really count: the art of combinatorial proof. Dolciani Mathematical Expositions 27 (Math. Assoc. Amer., Washington, DC, 2003).Google Scholar
5. Rymer, N.W., Projects, problems, and patience, Math. Gaz. 63 (March 1979) pp. 1–7.Google Scholar
6. MacKinnon, N., Note 73.28: An algebraic tiling proof, Math. Gaz. 73 (October 1989) pp. 210–211.Google Scholar
7. MacKinnon, N., Some thoughts on polyomino tiles, Math. Gaz. 74 (March 1990) pp. 31–33.Google Scholar
8. Sylvester, J.R., Note 86.02: Painting by numbers or polyominoes revisited, Math. Gaz., 86 (March 2002) pp. 68–72.Google Scholar
9. Temperley, H.N.V., Statistical mechanics and the partition of numbers II: The form of crystal surfaces, Proc. Cambridge Philos. Soc. 48 (1952) pp. 683–697.Google Scholar
10. Rogers, D.G., Things fall apart: a recurrence of tiling, The Mathematics Teacher 99 (2005) pp. 134–139.Google Scholar
11. Temperley, H.N.V., Combinatorial problems suggested by the statistical mechanics of domains and of rubber-like molecules, Phys. Rev. (2) 103 (1956) pp. 1–16.Google Scholar
12. Sharp, J., Have you seen this number? Math. Gaz. 82 (July 1998) pp. 203–214.Google Scholar
13. Lloyd, E.K., Letter regarding [12], Math. Gaz. 83 (March 1999) p. 134.Google Scholar
14. Sloane, N.J.A., The on-line encyclopaedia of integer sequences, http://www.research.att.com/~njas/sequences/Google Scholar