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US Math Competition Association
2021 USMCA
3
3
Part of
2021 USMCA
Problems
(1)
2021 USMCA National Championship #3
Source:
5/9/2021
Let
f
(
n
)
f(n)
f
(
n
)
be a sequence of integers defined by
f
(
1
)
=
1
,
f
(
2
)
=
1
,
f(1)=1, f(2)=1,
f
(
1
)
=
1
,
f
(
2
)
=
1
,
and
f
(
n
)
=
f
(
n
−
1
)
+
(
−
1
)
n
f
(
n
−
2
)
f(n)=f(n-1)+(-1)^nf(n-2)
f
(
n
)
=
f
(
n
−
1
)
+
(
−
1
)
n
f
(
n
−
2
)
for all integers
n
≥
3.
n \geq 3.
n
≥
3.
What is the value of
f
(
20
)
+
f
(
21
)
?
f(20)+f(21)?
f
(
20
)
+
f
(
21
)?