[seqfan] Re: Brick sequences

[N. J. A. Sloane]

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 1,1,1,2,3,4,5,6,7,9,11,15,20,27,35,44,56,73,91,115,148,186,227,283,358,435,
%T A005577 538,671,813,1001,1233,1492,1815,2223,2673,3247,3933,4713,5683,6850,8170,9785
%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