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11
Math Prize 2011 Problem 11
Math Prize 2011 Problem 11
Source:
September 19, 2011
linear algebra
matrix
algebra
polynomial
trigonometry
Problem Statement
The sequence
a
0
a_0
a
0
,
a
1
a_1
a
1
,
a
2
a_2
a
2
,
…
\ldots\,
…
satisfies the recurrence equation
a
n
=
2
a
n
−
1
−
2
a
n
−
2
+
a
n
−
3
a_n = 2 a_{n-1} - 2 a_{n - 2} + a_{n - 3}
a
n
=
2
a
n
−
1
−
2
a
n
−
2
+
a
n
−
3
for every integer
n
≥
3
n \ge 3
n
≥
3
. If
a
20
=
1
a_{20} = 1
a
20
=
1
,
a
25
=
10
a_{25} = 10
a
25
=
10
, and
a
30
=
100
a_{30} = 100
a
30
=
100
, what is the value of
a
1331
a_{1331}
a
1331
?
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