# [seqfan] Re: Brick sequences

franktaw at netscape.net franktaw at netscape.net
Sun Oct 25 18:07:28 CET 2009

```http://www.research.att.com/~njas/sequences/A001524 is, in fact, very
similar.  However, this requires that the pennies in each row be
contiguous, which I do not want to require.

There are some other sequence A005575, A005576, and A005577 which might
be related, but their descriptions say to see the references for
precise definition, so I don't know exactly what they are.  Certainly
none of them matches my values.

-----Original Message-----
From: N. J. A. Sloane <njas at research.att.com>

There is a paper that I saw and took sequences from
some time in the last 45 years  (see references below) which counts
stacks of
pennies

each row has to sit on gaps in the row below it

the pennies are on a sheet of paper, flat, and we are
looking down on them

the bottom layer has a certain number of adjacent pennies

the next row sits on them

and so on

for 6 pennies we could have

O O O O O O     1

O
O O O O O       4 ways

O   O
O O O O         3 ways

O
O O
O O O           1 way

for a total of 9

Sounds like a similar problem to the brick problem

Neil

Here's one sequence of this type, probably not
exactly the one I described, but the references should help:

%I A005577 M0495
%S A005577
1,1,1,2,3,4,5,6,7,9,11,15,20,27,35,44,56,73,91,115,148,186,227,283,358,43
5,
%T A005577
538,671,813,1001,1233,1492,1815,2223,2673,3247,3933,4713,5683,6850,8170,9
785
%N A005577 Number of arrangements of pennies in rows (see references
for precise
definition).
%D A005577 F. C. Auluck, On some new types of partitions associated
with
generalized Ferrers gr\
aphs. Proc. Cambridge Philos. Soc. 47, (1951), 679-686.
%D A005577 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of
Integer
ress, 1995 (includes this sequence).
%D A005577 E. M. Wright, Stacks, III, Quart. J. Math. Oxford, 23
(1972),
153-158.
%Y A005577 Cf. A005575, A005576.
%Y A005577 Sequence in context: A026445 A030151 A131617 this_sequence
A072966
A059759 A042952
%Y A005577 Adjacent sequences: A005574 A005575 A005576 this_sequence
A005578
A005579 A005580
%K A005577 nonn,nice,more
%O A005577 1,4
%A A005577 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy

```