Two messgaes

[Robert G. Wilson v]

Dear Antreas,

        A027649 begins with just a single one (1, 4, 14, 46, 146, ...), where as
your sequence began with two ones (1, 1, 4, 14, 46, 146, ...).

"Antreas P. Hatzipolakis" wrote:

> 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