Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of a conjecture of Stanley about Stern's array   Stanley, building on work of Stern, defined an array of numbers by the
recurrence $s(n, 2k) = s(n-1, k)$, $s(n, 2k+1) = s(n-1, k) + s(n-1, k+1)$.
Stanley showed that, for each positive integer $r$, the sequence $s_n^r:=
\sum_k s(n,k)^r$ obeys a homogeneous linear recurrence in $n$ of length
$r/2+O(1)$. Numerical evidence, however, suggested that $s_n^r$ obeys shorter
recurrences, of length $r/3+O(1)$. We prove Stanley's conjecture.

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The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
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The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc