# [seqfan] Re: Brick sequences

franktaw at netscape.net franktaw at netscape.net
Sat Oct 24 14:59:41 CEST 2009

```No; it's http://research.att.com/~njas/sequences/A000009

For n=9, you are missing [4,3,2].

-----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 ?

```