Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Identities involving the tribonacci numbers squared via tiling with
  combs   The number of ways to tile an $n$-board (an $n\times1$ rectangular board)
with $(\frac12,\frac12;1)$-, $(\frac12,\frac12;2)$-, and
$(\frac12,\frac12;3)$-combs is $T_{n+2}^2$ where $T_n$ is the $n$th tribonacci
number. A $(\frac12,\frac12;m)$-comb is a tile composed of $m$ sub-tiles of
dimensions $\frac12\times1$ (with the shorter sides always horizontal)
separated by gaps of dimensions $\frac12\times1$. We use such tilings to obtain
quick combinatorial proofs of identities relating the tribonacci numbers
squared to one another, to other combinations of tribonacci numbers, and to the
Fibonacci, Narayana's cows, and Padovan numbers. Most of these identities
appear to be new.

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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat