What is the recurrence relation for the following situation?
$begingroup$
Let $a_n$ be the number of non negative integer solutions to $x+y+z=n$ where $x$ is even.
For $n=0$: $a_0= 1$ ($0+0+0=0$)
For $n=1$: $a_1 = 2$ ($0+1+0=1$ or $0+0+1=1$)
For $n=2$: $a_2 = 4$ ($0+2+0=2$, $0+0+2=2$, $2+0+0=2$, or $0+1+1=2$)
recurrence-relations recursion
edited Dec 6 '18 at 23:38
SZN
2,708720
asked Dec 6 '18 at 23:32
Ethan AgranoffEthan Agranoff
1
$endgroup$
add a comment |
$begingroup$
Let $a_n$ be the number of non negative integer solutions to $x+y+z=n$ where $x$ is even.
For $n=0$: $a_0= 1$ ($0+0+0=0$)
For $n=1$: $a_1 = 2$ ($0+1+0=1$ or $0+0+1=1$)
For $n=2$: $a_2 = 4$ ($0+2+0=2$, $0+0+2=2$, $2+0+0=2$, or $0+1+1=2$)
recurrence-relations recursion
edited Dec 6 '18 at 23:38
SZN
2,708720
asked Dec 6 '18 at 23:32
Ethan AgranoffEthan Agranoff
1
$endgroup$
$begingroup$
what happens if you continue doing a few more experiments? Does a pattern emerge?
$endgroup$
– SZN
Dec 6 '18 at 23:36
add a comment |
$begingroup$
Let $a_n$ be the number of non negative integer solutions to $x+y+z=n$ where $x$ is even.
For $n=0$: $a_0= 1$ ($0+0+0=0$)
For $n=1$: $a_1 = 2$ ($0+1+0=1$ or $0+0+1=1$)
For $n=2$: $a_2 = 4$ ($0+2+0=2$, $0+0+2=2$, $2+0+0=2$, or $0+1+1=2$)
recurrence-relations recursion
edited Dec 6 '18 at 23:38
SZN
2,708720
asked Dec 6 '18 at 23:32
Ethan AgranoffEthan Agranoff
1
$endgroup$
Let $a_n$ be the number of non negative integer solutions to $x+y+z=n$ where $x$ is even.
For $n=0$: $a_0= 1$ ($0+0+0=0$)
For $n=1$: $a_1 = 2$ ($0+1+0=1$ or $0+0+1=1$)
For $n=2$: $a_2 = 4$ ($0+2+0=2$, $0+0+2=2$, $2+0+0=2$, or $0+1+1=2$)
recurrence-relations recursion
recurrence-relations recursion
edited Dec 6 '18 at 23:38
SZN
2,708720
asked Dec 6 '18 at 23:32
Ethan AgranoffEthan Agranoff
1
edited Dec 6 '18 at 23:38
SZN
2,708720
asked Dec 6 '18 at 23:32
Ethan AgranoffEthan Agranoff
1
edited Dec 6 '18 at 23:38
SZN
2,708720
edited Dec 6 '18 at 23:38
SZN
2,708720
edited Dec 6 '18 at 23:38
SZN
2,708720
2,708720
asked Dec 6 '18 at 23:32
Ethan AgranoffEthan Agranoff
1
asked Dec 6 '18 at 23:32
Ethan AgranoffEthan Agranoff
1
asked Dec 6 '18 at 23:32
Ethan AgranoffEthan Agranoff
1
1
$begingroup$
what happens if you continue doing a few more experiments? Does a pattern emerge?
$endgroup$
– SZN
Dec 6 '18 at 23:36
add a comment |
$begingroup$
what happens if you continue doing a few more experiments? Does a pattern emerge?
$endgroup$
– SZN
Dec 6 '18 at 23:36
$begingroup$
what happens if you continue doing a few more experiments? Does a pattern emerge?
$endgroup$
– SZN
Dec 6 '18 at 23:36
$begingroup$
what happens if you continue doing a few more experiments? Does a pattern emerge?
$endgroup$
– SZN
Dec 6 '18 at 23:36
add a comment |
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$begingroup$
what happens if you continue doing a few more experiments? Does a pattern emerge?
$endgroup$
– SZN
Dec 6 '18 at 23:36