On Reciprocal Series of Generalized Fibonacci Numbers with Subscripts in Arithmetic Progression

Alternating sums of reciprocal generalized Fibonacci numbers

ABSTRACT Recently Holliday and Komatsu extended the results of Ohtsuka and Nakamura on reciprocal sums of Fibonacci numbers to reciprocal sums of generalized Fibonacci numbers. The aim of this work is to give similar results for the alternating sums of reciprocals of the generalized Fibonacci numbers with indices in arithmetic progression. Finally we note our generalizations of some results of ...

Notes on Reciprocal Series Related to Fibonacci and Lucas Numbers

1 V5 Sn ^O^2IH-I + 2 / V 5 41oga (log a) ( ^ 2 ^ ^ + 2 ) ' and Almkvist [1] also gave an estimate of another series, i.e., 1 1 , 1 ' n '<+ ^ 0 4 „ + 2 8 41oga ( loga) 2 (^ 2 ( l o g a r l -2) ' In this paper, we continue this work and obtain some new results of similar kinds. In Section 2, some identities related to Fibonacci and Lucas numbers, which may be compared with the ones of [2] and [3]...

On k-Fibonacci numbers of arithmetic indexes

In this paper, we study the sums of k-Fibonacci numbers with indexes in an arithmetic sequence, say anþ r for fixed integers a and r. This enables us to give in a straightforward way several formulas for the sums of such numbers. 2008 Elsevier Inc. All rights reserved.

ON r-GENERALIZED FIBONACCI NUMBERS

GENERALIZED q - FIBONACCI NUMBERS

We introduce two sets of permutations of {1, 2, . . . , n} whose cardinalities are generalized Fibonacci numbers. Then we introduce the generalized q-Fibonacci polynomials and the generalized q-Fibonacci numbers (of first and second kind) by means of the major index statistic on the introduced sets of permutations.