duplicate hunting, pt. 15

Jon Schoenfield jonscho at hiwaay.net
Sun May 13 08:23:33 CEST 2007

```Joshua,

> My amateurish calculations seem to show that they are two different
> definitions of the same sequence.

Well, as perhaps the only real amateur on the mailing list (my only degree
is a BS in mechanical engineering ... but I'm a nice guy, anyway <g>), I'll
go ahead 'n' ask my notationally-challenged questions, and hope I don't
annoy anyone ...    :-)

Given the definitions

A024371(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [
(n+1)/2 ], s = A023532, t = (F(2), F(3), ...).
A025067(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [
n/2 ], s = A023532, t = (Fibonacci numbers).

... does the notation "t = (F(2), F(3), ...)" in the definition of A024371
mean the same thing as the notation "t = (Fibonacci numbers)" in the
definition of A025067?  If so, then I can see how, e.g., at n = 4, where I
get

A024371(4) = s(1)t(4) + s(2)t(3), where s = A023532, t = (F(2), F(3),
...).
A025067(4) = s(1)t(4) + s(2)t(3), where s = A023532, t = (Fibonacci
numbers).

... those, of course, would be the same number.  But then what about odd
values of n, e.g., n = 3, where I get

A024371(3) = s(1)t(3) + s(2)t(2), where s = A023532, t = (F(2), F(3),
...).
A025067(3) = s(1)t(3), where s = A023532, t = (Fibonacci numbers).

...?  How could these be the same?   ?:-/

'Sorry if I'm being specific-gravity-enhanced (i.e., dense) ...

-- Jon

----- Original Message -----
From: "Joshua Zucker" <joshua.zucker at gmail.com>
To: "Jon Schoenfield" <jonscho at hiwaay.net>
Cc: "Andrew Plewe" <aplewe at sbcglobal.net>; <seqfan at ext.jussieu.fr>
Sent: Sunday, May 13, 2007 12:41 AM
Subject: Re: duplicate hunting, pt. 15

> On 5/12/07, Jon Schoenfield <jonscho at hiwaay.net> wrote:
>> > A025067 and A024371
>>
>> This reminds me of the situation with two other sequences by the same
>> author -- A024468 and A025080 (the latter of which has since been changed
>> to
>> keyword:dead).  I think we concluded that A025080's terms didn't agree
>> with
>> the definition it had had before it was changed to its current definition
>> of
>> "Duplicate of A024468" ....
>>
>> Of A025067 and A024371, is it the case that one of the definitions really
>> yields the sequence 1, 2, 3, 5, 11, 18, etc., and the other doesn't?  Or
>> are
>> they both wrong?
>
> My amateurish calculations seem to show that they are two different
> definitions of the same sequence.
>
> --Joshua Zucker
>
>

```