[seqfan] Re: A005479 and A153867

[Graeme McRae]

I discovered (or re-discovered, if it's well known) a generalization to
this relationship between Lucas and Fibonacci numbers, namely

L(n) = F(n) + F(n-1) + F(n-2) + F(n-3)

The generalization can be expressed this way:

"The sum of the 2m consecutive Fibonacci numbers F(n-m-1) thru F(n+m-2) is
F(n)*L(m) if m is odd, and L(n)*F(m) if m is even."

The above statement is the special case when m=2

A quick look at A000045 (Fibonacci) and A000032 (Lucas) makes me think this
fact isn't referenced in either sequence.


--Graeme McRae
Palmdale, CA


On Thu, Apr 24, 2014 at 2:14 PM, Graeme McRae <graememcrae at gmail.com> wrote:

> The Lucas numbers already have that comment, expressed this way:
> L(n) = F(n) + F(n-1) + F(n-2) + F(n-3)
>
> --Graeme McRae
> Palmdale, CA
>
>
> On Thu, Apr 24, 2014 at 12:07 PM, Harvey P. Dale <hpd at hpdale.org> wrote:
>
>> Vladimir:
>>         Thanks.  Perhaps you could add that to each of the sequences, and
>> also make sure that each cross-references the other?
>>         Best,
>>         Harvey
>>
>>
>> -----Original Message-----
>> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of
>> Vladimir Shevelev
>> Sent: Thursday, April 24, 2014 10:19 AM
>> To: Sequence Fanatics Discussion list
>> Subject: [seqfan] Re: A005479 and A153867
>>
>> Or simply it follows from the identity F(n)+F(n+1)+F(n+2)+F(n+3) =
>> A000032(n+3), n>=0.
>>
>> Regards,
>> Vladimir
>>
>> ________________________________________
>> From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of L. Edson
>> Jeffery [lejeffery2 at gmail.com]
>> Sent: 23 April 2014 20:40
>> To: seqfan at list.seqfan.eu
>> Subject: [seqfan] Re: A005479 and A153867
>>
>> Harvey,
>>
>> They are the same except the first two terms of A005479 (cf. the formula
>> by
>> Mathar): A153867(n) = A005479(n+2).
>>
>> Ed Jeffery
>>
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