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Re: a[n],b[n]

• To: mathgroup at smc.vnet.net
• Subject: [mg104909] Re: [mg104889] a[n],b[n]
• From: Leonid Shifrin <lshifr at gmail.com>
• Date: Fri, 13 Nov 2009 05:53:08 -0500 (EST)
• References: <200911121107.GAA19027@smc.vnet.net>

Your coefficients represent a rotation matrix with the angle Pi/5.
Therefore, the answers are:

a[n]  = 4 Cos[(n \[Pi])/5] - 9 Sin[(n \[Pi])/5]

b[n] = 9 Cos[(n \[Pi])/5] + 4 Sin[(n \[Pi])/5],

where I started counting from zero:

a[0] = 4, b[0] = 9.


Regards,
Leonid


On Thu, Nov 12, 2009 at 3:07 AM, ynb <wkfkh056 at yahoo.co.jp> wrote:

> 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]=
>
>

• References:
  • a[n],b[n]
    • From: ynb <wkfkh056@yahoo.co.jp>