Journal of Integer Sequences, Vol. 13 (2010), Article 10.5.8 |

Graduate School of Science and Technology

Hirosaki University

Hirosaki, 036-8561

Japan

Vichian Laohakosol

Department of Mathematics

Kasetsart University

Bangkok 10900

Thailand

**Abstract:**

We discuss the partial infinite sum
for
some positive integer , where satisfies a recurrence relation
of order ,
(),
with initial values ,
(
),
where and are positive integers. If , , and
, , then is the -th Fibonacci number. Our
results include some extensions of Ohtsuka and Nakamura. We also
consider continued fraction expansions that include such infinite
sums.

(Concerned with sequence A000073.)

Received January 20 2010;
revised version received May 19 2010.
Published in *Journal of Integer Sequences*, May 20 2010.

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