Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double-Recurrence Fibonacci Numbers and Generalizations   Let $(F_n)_{n\geq 0}$ be the Fibonacci sequence given by the recurrence
$F_{n+2}=F_{n+1}+F_n$, for $n\geq 0$, where $F_0=0$ and $F_1=1$. There are
several generalizations of this sequence and also several interesting
identities. In this paper, we investigate a homogeneous recurrence relation
that, in a way, extends the linear recurrence of the Fibonacci sequence for two
variables, called {\it double-recurrence Fibonacci numbers}, given by ${F(m,n)
= F(m-1, n-1)+F (m-2, n-2)}$, for $n,m\geq 2$, where $F (m, 0) = F_m$, $F (m,
1) = F_{m+1}$, $F (0, n) = F_n$ and $F (1, n) = F_{n+1}$. We exhibit a formula
to calculate the values of this double recurrence, only in terms of Fibonacci
numbers, such as certain identities for their sums are outlined. Finally, a
general case is studied.

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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga