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Fibonacci numbers

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1: 26.11 Integer Partitions: Compositions
The Fibonacci numbers are determined recursively by …
26.11.6 c ( T , n ) = F n - 1 , n 1 .
26.11.7 F n = ( 1 + 5 ) n - ( 1 - 5 ) n 2 n 5 .
Additional information on Fibonacci numbers can be found in Rosen et al. (2000, pp. 140–145).
2: 24.15 Related Sequences of Numbers
§24.15(iv) Fibonacci and Lucas Numbers
The Fibonacci numbers are defined by u 0 = 0 , u 1 = 1 , and u n + 1 = u n + u n - 1 , n 1 . …
24.15.11 k = 0 n / 2 ( n 2 k ) ( 5 9 ) k B 2 k u n - 2 k = n 6 v n - 1 + n 3 n v 2 n - 2 ,
For further information on the Fibonacci numbers see §26.11.
3: Bibliography K
  • R. P. Kelisky (1957) On formulas involving both the Bernoulli and Fibonacci numbers. Scripta Math. 23, pp. 27–35.
  • 4: Bibliography H
  • K. Horata (1989) An explicit formula for Bernoulli numbers. Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.
  • K. Horata (1991) On congruences involving Bernoulli numbers and irregular primes. II. Rep. Fac. Sci. Technol. Meijo Univ. 31, pp. 1–8.
  • F. T. Howard (1996a) Explicit formulas for degenerate Bernoulli numbers. Discrete Math. 162 (1-3), pp. 175–185.
  • F. T. Howard (1996b) Sums of powers of integers via generating functions. Fibonacci Quart. 34 (3), pp. 244–256.
  • I. Huang and S. Huang (1999) Bernoulli numbers and polynomials via residues. J. Number Theory 76 (2), pp. 178–193.