[seqfan] Re: A sort of composition

[Rob Pratt]

The next two terms are 344 and 856, and that is enough to reduce the candidates to the two essentially identical ones out of the four.

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of David Newman
Sent: Monday, August 18, 2014 9:53 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] A sort of composition

Count the number of compositions of n arranged in an array for which each row length is less than or equal to the length of the row above it.
(Similar to a plane partition,but with no restriction that the summands be decreasing along rows and columns.)

For example: for 3 there are 8 such compositions
3

2,1

1,2

2
1

1
2

1,1,1

1,1
1

1
1
1

The first few values that I get are 1,3,8,21,54,137

This matches four sequences in the OEIS, but it doesn't match any of the definitions, as far as I can see .  Can someone out there tell me if it's the same as one of the matches?

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