| 释义 |
Fibonacci n-Step NumberAn  -step Fibonacci sequence is given by defining  for  ,  ,  , and
 | (1) |
 . The case  corresponds to the degenerate 1, 1, 2, 2, 2, 2 ...,  to the usual FibonacciNumbers 1, 1, 2, 3, 5, 8, ... (Sloane's A000045),  to the A000073),  to the Tetranacci Numbers1, 1, 2, 4, 8, 15, 29, 56, 108, ... (Sloane's A000078), etc.
The limit  is given by solving
 | (2) |
 and taking the Real Root  . If , the equation reduces to
 | (3) |
 | (4) |
 | (5) |
 | (6) |
 .See also Fibonacci Number, Tribonacci Number
References
Sloane, N. J. A. SequencesA000045/M0692,A000073/M1074, andA000078/M1108in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
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