What is the recurrence relation for the following situation?

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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 $0+1+1=2$)










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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
















0












$begingroup$


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 $0+1+1=2$)










share|cite|improve this question











$endgroup$












  • $begingroup$
    what happens if you continue doing a few more experiments? Does a pattern emerge?
    $endgroup$
    – SZN
    Dec 6 '18 at 23:36














0












0








0





$begingroup$


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 $0+1+1=2$)










share|cite|improve this question











$endgroup$




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






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edited Dec 6 '18 at 23:38









SZN

2,713720




2,713720










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


















  • $begingroup$
    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










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