kth order Fibonacci numbers

(definition)

Definition: A sequence of numbers where each number is the sum of the k preceding numbers. The usual Fibonacci numbers occur when k=2.

Formal Definition:

• F^(k)_n = F^(k)_n-1 + F^(k)_n-2 + . . . + F^(k)_n-k      for n ≥ k.
• F^(k)_k-1 = 1
• F^(k)_n = 0      for   0 ≤ n ≤ k-2

Also known as pth order Fibonacci numbers.

See also optimal polyphase merge.

Author: PEB

More information

Apparently first studied by V. Schlegel, El Progreso Matemático, 4:173-174, 1894.

If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.

Entry modified 17 December 2004.
HTML page formatted Fri Mar 25 16:20:34 2011.

Cite this as:
Paul E. Black, "kth order Fibonacci numbers", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 17 December 2004. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/kthOrderFibonacci.html