[seqfan] Re: sequence from a test A171371

[Alexander Povolotsky]

PURRS Demo Results
Exact solution for x(n) = 6*x(-1+n)+8*x(-2+n)
for the initial conditions
x(1) = 8
x(2) = 18
x(n) = -15/8*(3-sqrt(17))^n-15/8*(3+sqrt(17))^n+77/136*(3+sqrt(17))^n*sqrt(17)-77/136
*(3-sqrt(17))^n*sqrt(17)
for each n >= 1

so explicit formula appears to be

a(n)= -15/8*(3-sqrt(17))^n-15/8*(3+sqrt(17))^n+77/136*(3+sqrt(17))^n*sqrt(17)-77/136
*(3-sqrt(17))^n*sqrt(17)

ARP

On 12/6/09, zak seidov <zakseidov at yahoo.com> wrote:
> a(n)=6*a(n-1)+8*a(n-2)
>
> --- On Sun, 12/6/09, N. J. A. Sloane <njas at research.att.com> wrote:
>
>> From: N. J. A. Sloane <njas at research.att.com>
>> Subject: [seqfan]  sequence from a test
>> To: seqfan at seqfan.eu
>> Date: Sunday, December 6, 2009, 11:35 PM
>>
>> Dear SeqFans,  I don't know the answer - can anyone
>> help?
>> Neil
>>
>> %I A171371
>> %S A171371
>> 8,18,172,1176,8432,60000,427456,3044736,21688064,154486272
>> %N A171371 I don't know the pattern to this sequence yet,
>> but it appears on mental-testing.com.
>> %K A171371 nonn
>> %O A171371 1,1
>> %A A171371 Parkers (Parkersfat(AT)yahoo.com), Dec 06 2009
>>
>>
>>
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