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Putnam
1990 Putnam
A1
Sum of well-known sequences
Sum of well-known sequences
Source: Putnam 1990 A1
July 12, 2013
Putnam
college contests
Problem Statement
Let
T
0
=
2
,
T
1
=
3
,
T
2
=
6
,
T_0=2, T_1=3, T_2=6,
T
0
=
2
,
T
1
=
3
,
T
2
=
6
,
and for
n
≥
3
n\ge 3
n
≥
3
,
T
n
=
(
n
+
4
)
T
n
−
1
−
4
n
T
n
−
2
+
(
4
n
−
8
)
T
n
−
3
.
T_n=(n+4)T_{n-1}-4nT_{n-2}+(4n-8)T_{n-3}.
T
n
=
(
n
+
4
)
T
n
−
1
−
4
n
T
n
−
2
+
(
4
n
−
8
)
T
n
−
3
.
The first few terms are
2
,
3
,
6
,
14
,
40
,
152
,
784
,
5158
,
40576
,
363392.
2, 3, 6, 14, 40, 152, 784, 5158, 40576, 363392.
2
,
3
,
6
,
14
,
40
,
152
,
784
,
5158
,
40576
,
363392.
Find a formula for
T
n
T_n
T
n
of the form
T
n
=
A
n
+
B
n
,
T_n=A_n+B_n,
T
n
=
A
n
+
B
n
,
where
{
A
n
}
\{A_n\}
{
A
n
}
and
{
B
n
}
\{B_n\}
{
B
n
}
are well known sequences.
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