RE: a[n],b[n]

• To: mathgroup at smc.vnet.net
• Subject: [mg104912] RE: [mg104889] a[n],b[n]
• From: Tomas Garza <tgarza10 at msn.com>
• Date: Fri, 13 Nov 2009 05:53:42 -0500 (EST)
• References: <200911121107.GAA19027@smc.vnet.net>

```Presumably the lack of natural language in your question arises from the fact that you speak only Japanese (judging from your mail address). I will assume that as an explanation and hence suggest that you use RSolve and evaluate

RSolve[{a[n+1]==1/4*(1+Sqrt[5])*a[n]-1/2*Sqrt[1/2*(5-Sqrt[5])]*b[n],b[n+1]==1/2*Sqrt[1/2*(5-Sqrt[5])]*a[n]+1/4*(1+Sqrt[5])*b[n],a[1]==
4,b[1]==9},{a[n],b[n]},n]

Tomas

> Date: Thu, 12 Nov 2009 06:07:30 -0500
> From: wkfkh056 at yahoo.co.jp
> Subject: [mg104889] a[n],b[n]
> To: mathgroup at smc.vnet.net
>
> a[n + 1] = 1/4*(1 + Sqrt[5])*a[n] - 1/2*Sqrt[1/2*(5 - Sqrt[5])]*b[n],
> b[n + 1] = 1/2*Sqrt[1/2*(5 - Sqrt[5])]*a[n] + 1/4*(1 + Sqrt[5])*b[n],
> a[1] = 4, b[1] = 9.
>
>
> a[n]=
> b[n]=
>

```

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