Two messgaes

[Antreas P. Hatzipolakis]

Dear Robert

You wrote:

>Dear Antreas,
>
>        The first sequence is A051178 in Neil J.A. Sloane's Online Electronic
                                ^^^^^^

Quite recent, I think!
(Perhaps Neil added it in the _EIS_ after my 19-Oct-99 message)


>Integer Sequence.
>
>
>http://akpublic.research.att.com:80/~njas/sequences/
>
>        The second sequence is A(-2) = A(-1) =1, A(n) = 3*A(n-1) + 2^n.  I am
>not entirely happy with this 'definition.'

and is the sequence  A027649 in _EIS_

>
>Sequentially yours,
>
>Robert G. Wilson v,
>Ph.D. ATP / CF&GI


Greetings from Athens

Antreas


>"Antreas P. Hatzipolakis" wrote:
>
>> FWD MESSAGE ------------------------------------------------------------
>>
>> Subject: Re: Describe These Numbers (solution)
>> From: Leroy Quet <qqquet at hotbot.com>
>> Date: 19 Oct 99 13:53:06 -0400 (EDT)
>> Newsgroup: sci.math
>>
>> I, Leroy Quet wrote:
>>
>> >Inspired by Clive Tooth's post, I give you my own number puzzle.
>> >Find the simplest definition for the following numbers.
>> >I've included all of them <=100.
>> >
>> >1,2,4,6,8,10,12,16,18,20,24,27,28,30,32,36,40,42,45,48,
>> >52,54,56,60,64,66,70,72,76,78,80,82,84,90,96,100
>> >
>> >I'll post my solution soon if no one else solves it sooner.
>>
>> These numbers are the positive integers, n, where the number of
>> positive divisors of n! is divisible by n.
>> Thanks,
>> Leroy Quet
>>
>> END ------------------------------------------------------------------------
>>
>> and one from a friend:
>>
>> <quote>
>>      A colleague of mine presented me with a sequence and challenged me to
>> find the recursion formula for it.
>> After trying several known techniques - I began to 'cheat' and looked
>> in my copy of Sloane's encyclopedia - to no avail.
>> Can you help?
>> 1    1    4    14    46    146    454    (1394)    (4246)
>>                                          ^^^^^^^^^^^^^^^^
>>                                    My predictions based on my work.
>> </quote>
>>
>> Antreas