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Horadam Sequence

A Horadam sequence is a generalization of the Fibonacci numbers defined by the four constants (p,q,r,s) and the definitions H_0=p and H_1=q together with the linear recurrence equation

H_n=sH_(n-1)+rH_(n-2)

for n>1. With p=0, q=1, r=1, and s=1, the Horadam sequence reduces to the Fibonacci numbers.

See also

Fibonacci Number

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References

Horadam, A. F. "Basic Properties of a Certain Generalised Sequence of Numbers." Fib. Quart. 3, 161-176, 1965.Horadam, A. F. "Special Properties of the Sequence W_n(a,b;p,q)." Fib. Quart. 5, 424-434, 1967. https://doi.org/10.1080/00150517.1967.12431271.Horadam, A. F. "Jacobsthal Representations Numbers." Fib. Quart. 34, 40-54, 1996.Reiter, C. A. "Exact Horadam Numbers with a Chebyshevish Accent." Vector 16, 122-131, 1999.

Referenced on Wolfram|Alpha

Horadam Sequence

Cite this as:

Weisstein, Eric W. "Horadam Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HoradamSequence.html

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