Abstract
There are many ways to generalize the well-known Fibonacci sequence {Fn}, Fn = Fn-1 + Fn-2, F1 = 1, F2 = 1. In a personal letter dated December 18, 1985, Frank Harary asked one of the authors if they had ever encountered Cn = Cn-1 + Cn-2 + 1, which was used by Harary in connection with something he was counting involving Boolean Algebras. In fact, in Harary’s research it was noticed that the value of one could be replaced by any integer k.
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References
Horibe, Y. ”An Entropy View of Fibonacci Trees.” The Fibonacci Quarterly, Vol. 2Ø, No. 2 (1982): pp 168–178.
Horibe, Y. ”Notes on Fibonacci Trees and Their Optimality.” The Fibonaccl Quarterly, Vol. 21, No. 2 (1983): pp 118–128.
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© 1988 Springer Science+Business Media New York
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Bicknell-Johnson, M., Bergum, G.E. (1988). The Generalized Fibonacci Numbers {Cn}, Cn = Cn-1 + Cn-2 + K. In: Philippou, A.N., Horadam, A.F., Bergum, G.E. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7801-1_18
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DOI: https://doi.org/10.1007/978-94-015-7801-1_18
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