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9
Explicit formula for a_n
Explicit formula for a_n
Source:
September 15, 2010
algebra
Sequence
Recurrence
recurrence relation
IMO Shortlist
Problem Statement
A sequence
(
a
n
)
(a_n)
(
a
n
)
is defined by means of the recursion
a
1
=
1
,
a
n
+
1
=
1
+
4
a
n
+
1
+
24
a
n
16
.
a_1 = 1, a_{n+1} = \frac{1 + 4a_n +\sqrt{1+ 24a_n}}{16}.
a
1
=
1
,
a
n
+
1
=
16
1
+
4
a
n
+
1
+
24
a
n
.
Find an explicit formula for
a
n
.
a_n.
a
n
.
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