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- The
-Fibonacci-
sequence (the
th term of which is denoted
)
is defined recursively by the following statements:
Note that this idea encompasses both the
-Fibonacci sequence and the Fibonacci-
sequence.
means that
has the following properties:
.
- For all
such that
, it follows that
.
is the least positive integer satisfying these properties.
means that
has the following properties:
- For all
such that
, it follows that
.
-
.
is the least positive integer satisfying these properties.
Note:
is then the function that gives the period of the
-Fibonacci-
sequence in modulo
.
-
means that
has the following properties:
is the number of
that satisfy the property that all
from
to
, inclusive, satisfy the property that
, where
goes from
to
, inclusive.
-
means that
has the following properties:
is the number of
that satisfy the property that all
from
to
, inclusive, satisfy the property that
, where
goes from
to
, inclusive.
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Up: k-Fibonacci-q numbers and new
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Gregory Stoll
2000-04-08