# [seqfan] Re: Brick sequences

Mitch Harris maharri at gmail.com
Sat Oct 24 22:22:59 CEST 2009

```So is the following pattern allowed? :

=     =
= = = = =

If so, then these might be counted by generalized Catalan #'s.

(paths from 0,0 to n,n below  x=y, with steps (0,1), (1,0), (1,1) ?)

Google for

Snevily West bricklaying problem

There is mention of this paper once in the OEIS, but in a seemingly
unrelated sequence.
The bricklaying problem seems recent enough that it's not mentioned in
Stanley.

Mitch Harris

> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu
> [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of
> franktaw at netscape.net
> Sent: Saturday, October 24, 2009 9:00 AM
> To: seqfan at list.seqfan.eu
> Subject: [seqfan] Re: Brick sequences
>
> No; it's http://research.att.com/~njas/sequences/A000009
>
> For n=9, you are missing [4,3,2].
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Jaume Oliver i Lafont <joliverlafont at gmail.com>
>
> If not only the mirror images are the same, but also we only care
> about the floor where each brick lays, i think it is the number of
> decreasing -equivalently, increasing- partitions.
>
> i get by hand these numbers, starting at n=1
> 1,1,2,2,3,4,5,6,7,10
>
> let [a,b,c] mean "a" bricks on the ground, "b" on first floor, "c" on
> second floor; then the cases are
>
> a(1)=1 : [1]
> a(2)=1 : [2]
> a(3)=2 : [3] and [2,1]
> a(4)=2 : [4] and [3,1]
> a(5)=3 : [5], [4,1] and [3,2]
> a(6)=4 : [6], [5,1], [4,2], [3,2,1]
> a(7)=5 : [7], [6,1], [5,2], [4,3], [4,2,1]
> a(8)=6 : [8], [7,1], [6,2], [5,3]  [5,2,1]  [4,3,1]
> a(9)=7 : [9], [8,1], [7,2], [6,3], [6,2,1]  [5,4], [5,3,1]
> a(n)=10: [10], [9,1], [8,2], [7,3], [7,2,1], [6,4] [6,3,1], [5,4,1],
> [5,3,2], [4,3,2,1]
>
> Is this an equivalent definition for
> http://research.att.com/~njas/sequences/A066639 ?
>
>
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```

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