Two messgaes

[Robert G. Wilson v]

Dear Antreas,

        The first sequence is A051178 in Neil J.A. Sloane's Online Electronic
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.'

Sequentially yours,

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

"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