Anthony Shannon’s research on Fibonacci-like objects

Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 4, 1998, Number 2, Pages 47—56
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Krassimir T. Atanassov
Math. Research Lab, P.O.Box 12,
Sofia-1113, BULGARIA

References

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  10. A. Shannon, A method of Carlitz applied to the k^ power generating function for Fibonacci numbers. The Fibonacci Quarterly, Vol. 12, 1974, No. 3, 293-299.
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  25. A. Shannon, Some lacunary recurrence relations. The Fibonacci Quarterly, Vol. 18, 1980, No. 1, 73-79.
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  27. J. Clarke, A. Shannon, Some constraints on Fermat’s last theorem. The Fibonacci Quarterly, Vol. 19, 1981, No. 4, 375-376.
  28. A. Shannon, A. Horadam, Concerning a paper by L. G. Wilson. The Fibonacci Quarterly, Vol. 20, 1982, No. 1, 38-41.
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  33. A. Shannon, A. Horadam, Infinite classes of sequence-generated circles. The Fibonacci Quarterly, Vol. 22, 1984, No. 3, 247-251.
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  38. A. Shannon, A. Horadam Generalized Fibonacci continued fractions. The Fibonacci Quarterly, Vol. 26, 1988, No. 3, 219-223.
  39. A. Horadam, A. Shannon, Asveld’s polynomials Pj(n). Applications of Fibonacci Numbers, Vol. 1 (A. Philippou at ah, Eds.), Kluver Academic Publishers, Dordrecht, 1988, 163-176.
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  41. J. Turner, A. Shannon On A^-order colored convolution trees and a generalized Zeckendorf integer representation theorem. The Fibonacci Quarterly, Vol. 27, 1989, No. 5, 439-447.
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    1990, 299-309.
  44. R. Whitaker, A. Shannon Some recursive asymptotes. The Fibonacci Quarterly, Vol. 29,
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  46. A. Shannon, Turner J., Atanassov K., A generalized tableau associated with colored convolution trees, Discrete Mathematics, Vol. 92, No. 1-3, Nov. 1991, 329-340.
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  48. A. Horadam, A. Shannon, Pell-type number generators of Pythagorean triples. Applications of Fibonacci Numbers, Vol. 5 (G. Bergumat ah, Eds.), Kluver Academic Publishers, Dordrecht, 1993, 331-343.
  49. C. Long, G. Cohen, T. Langtry, A. Shannon, Arithmetic sequences and second order recurrences. Applications of Fibonacci Numbers, Vol. 5 (G. Bergumat al., Eds.), Kluver Academic Publishers, Dordrecht, 1993, 449-457.
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  51. W. Hung, A. Shannon, B. Thornton, The use of a second-order recurrence relation in the diagnosis of breast cancer. The Fibonacci Quarterly, Vol. 32, 1994, No. 3, 253-259.
  52. R. Melham, A. Shannon Some congruence properties of generalized second-order integer sequences. The Fibonacci Quarterly, Vol. 32, 1994, No. 5, 424-428.
  53. R. Melham, A. Shannon Some infinite series summations using power series evaluated at a matrix. The Fibonacci Quarterly, Vol. 33, 1995, No. 1, 13-20.
  54. R. Melham, A. Shannon Inverse trigonometric and hyperbolic summation formulas involving generalized Fibonacci numbers. The Fibonacci Quarterly, Vol. 33, 1995, No. 1, 32-40.
  55. R. Melham, A. Shannon Some summation identities using generalized Q-matrices. The Fibonacci Quarterly, Vol. 33, 1995, No. 1, 64-73.
  56. R. Melham, A. Shannon A generalization of the Catalan identity and some consequences. The Fibonacci Quarterly, Vol. 33, 1995, No. 1, 82-84.
  57. R. Melham, A. Shannon Generalization of some simple congruences. The Fibonacci Quarterly, Vol. 33, 1995, No. 2, 126-130.
  58. R. Melham, A. Shannon On reciprocal sums of Chebyshev related sequences. The Fibonacci Quarterly, Vol. 33, 1995, No. 3, 194-202.
  59. K. Atanassov, Shannon A., Turner J., The generation of trees from coupled third order recurrence relations, Discrete Mathematics and Applications (S. Shtrakov and I. Mirchev, Eds.), Research in Mathematics, Vol. 5, Blagoevgrad, 1995, 46-56.
  60. F. Dubeau, A. Shannon A Fibonacci model of infectious disease. The Fibonacci Quarterly, Vol. 34, 1996, No. 3, 257-270.
  61. R. Melham, A. Shannon, On reciprocal sums of second order sequences. Applications of Fibonacci Numbers, Vol. 6 (G. Bergumat ah, Eds.), Kluver Academic Publishers, Dordrecht, 1996, 355-364.
  62. A. Shannon, R. Loh, R. Melham, A. Horadam, A search for solutions of a functional equation. Applications of Fibonacci Numbers, Vol. 6 (G. Bergumat al., Eds.), Kluver Academic Publishers, Dordrecht, 1996, 431-441.
  63. A. Shannon, I. Tang, R. Ollerton, A use of generalized Fibonacci numbers in finding quadratic factors. Applications of Fibonacci Numbers, Vol. 6 (G. Bergumat al., Eds.), Kluver Academic Publishers, Dordrecht, 1996, 443-450.
  64. K. Atanassov, Shannon A., Turner J., Remark on Fibonacci sequences and fuzzy sets, Comptes Rendus de l’Academie bulgare des Sciences, Tome 50, 1997, No. 2, 11-14.

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Atanassov, K. T. (1998). Anthony Shannon’s research on Fibonacci-like objects. Notes on Number Theory and Discrete Mathematics, 4(2), 47-56.

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