From: "N. J. A. Sloane" <njas@research.att.com>
Subject: Levine's sequence
Date: Fri, 28 Nov 1997 09:40:41 -0500 (EST)

Here is a /very/ simple recursive sequence, yet it seems likely 
that the 20th term say is impossible to compute.

Like other nice sequences, it begins by writing down 1,1

I describe the recurrence by an example:
after the row that says

   1,1,1,2,2,3,4

you read it from the right, and write down 4 ones, 3 twos,
2 threes,  2 fours, 1 five, 1 six and 1 seven, getting

   1,1,1,1,2,2,2,3,3,4,4,5,6,7

so the array looks like this:

1,1
1,2
1,1,2
1,1,2,3
1,1,1,2,2,3,4
1,1,1,1,2,2,2,3,3,4,4,5,6,7
etc

THE SEQUENCE is formed from the last terms of the array:

   1,2,2,3,4,7,14,42,213,2837,etc

I know only 15 terms:

1,2,2,3,4,7,14,42,213,2837,175450,139759600,6837625106787,
266437144916648607844,508009471379488821444261986503540

and as i said it may be impossible to calculate the 20th term!

Several people have worked on this sequence, which was discovered by
Lionel Levine, and there is a lot about it in the corresponding
entry in the sequence table ( see sequence A011784).  But I think it
deserves to be more widely known.

 Neil J. A. Sloane, njas@research.att.com,
 Note new address: AT&T Research Labs, Room C233, 180 Park Ave,
 Florham Park, NJ 07932-0971 USA.
 Home page: http://www.research.att.com/~njas/