MathDB
Problems
Contests
National and Regional Contests
India Contests
India EGMO TST
India EGMO 2023 TST
5
5
Part of
India EGMO 2023 TST
Problems
(1)
K-pop sequences
Source: India EGMO TST 2023/5
12/10/2022
Let
k
k
k
be a positive integer. A sequence of integers
a
1
,
a
2
,
⋯
a_1, a_2, \cdots
a
1
,
a
2
,
⋯
is called
k
k
k
-pop if the following holds: for every
n
∈
N
n \in \mathbb{N}
n
∈
N
,
a
n
a_n
a
n
is equal to the number of distinct elements in the set
{
a
1
,
⋯
,
a
n
+
k
}
\{a_1, \cdots , a_{n+k} \}
{
a
1
,
⋯
,
a
n
+
k
}
. Determine, as a function of
k
k
k
, how many
k
k
k
-pop sequences there are.Proposed by Sutanay Bhattacharya
combinatorics