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2011 VTRMC
Problem 2
recurrence relation: find a_100
recurrence relation: find a_100
Source: VTRMC 2011 P2
May 14, 2021
recurrence relation
algebra
Sequences
Problem Statement
A sequence
(
a
n
)
(a_n)
(
a
n
)
is defined by
a
0
=
−
1
,
a
1
=
0
a_0=-1,a_1=0
a
0
=
−
1
,
a
1
=
0
, and
a
n
+
1
=
a
n
2
−
(
n
+
1
)
2
a
n
−
1
−
1
a_{n+1}=a_n^2-(n+1)^2a_{n-1}-1
a
n
+
1
=
a
n
2
−
(
n
+
1
)
2
a
n
−
1
−
1
for all positive integers
n
n
n
. Find
a
100
a_{100}
a
100
.
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