kthordrfibon.html

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<H1>kth order Fibonacci numbers</H1>
<P>
(definition)

<P>
<strong>Definition:</strong>
A sequence of numbers where each number is the sum of the <em>k</em> preceding numbers. The usual <a href="fibonacnmbrs.html" tppabs="http://hissa.nist.gov/dads/HTML/fibonacnmbrs.html"><em>Fibonacci numbers</em></a> occur when <em>k=2</em>.
<P><strong>See also</strong>
<a href="optimpolymrg.html" tppabs="http://hissa.nist.gov/dads/HTML/optimpolymrg.html"><em>optimal polyphase merge</em></a>.
<P><em>Note:
These were apparently first studied by V. Schlegel in <em>El Progreso Matem&aacute;tico</em> <strong>4</strong> (1894), pages 173-174. <P> More formally the numbers are<BR> <em>F<sup>(k)</sup><sub>n</sub></em> = <em>F<sup>(k)</sup><sub>n-1</sub></em> + <em>F<sup>(k)</sup><sub>n-2</sub></em> + . . . + <em>F<sup>(k)</sup><sub>n-k</sub></em> &nbsp;&nbsp;&nbsp;&nbsp; for  n  <img src="geq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/geq.gif" border=0 height=7  width=14 alt="greater than or equal to"> k. <P> <em>F<sup>(k)</sup><sub>k-1</sub></em> = 1 <P> <em>F<sup>(k)</sup><sub>n</sub></em> = 0 &nbsp;&nbsp;&nbsp;&nbsp; for &nbsp;  0  <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7  width=14 alt="less than or equal to"> n  <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7  width=14 alt="less than or equal to"> k-2</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Tue Jun  8 11:16:54 1999.<BR>
HTML page formatted Wed Dec 22 09:35:40 1999.

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