[seqfan] Re: Brick sequences

[franktaw at netscape.net]

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.

Franklin T. Adams-Watters

-----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
Sequences, Academic P\
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