%I A001169 M1636 N0639
%S A001169 1,2,6,19,61,196,629,2017,6466,20727,66441,212980,682721,2188509,
%T A001169 7015418,22488411,72088165,231083620,740754589,2374540265,7611753682,
%U A001169 24400004911,78215909841,250726529556,803721298537,2576384425157
%N A001169 Number of board-pile polyominoes with n cells.
%C A001169 The inverse binomial transform is 1,1,3,6,..., i.e. the unsigned version 
               of A077926. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 15 
               2008
%D A001169 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001169 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001169 I. G. Enting and A. J. Guttmann, On the area of square lattice polygons, 
               J. Statist. Phys., 58 (1990), 475-484.
%D A001169 Dean Hickerson, Counting Horizontally Convex Polyominoes, J. Integer 
               Sequences, Vol. 2 (1999), #99.1.8.
%D A001169 D. A. Klarner, The number of graded partially ordered sets, J. Combin. 
               Theory, 6 (1969), 12-19.
%D A001169 W. F. Lunnon, Counting polyominoes, pp. 347-372 of A. O. L. Atkin and 
               B. J. Birch, editors, Computers in Number Theory. Academic Press, 
               NY, 1971.
%D A001169 R. P. Stanley, Enumerative Combinatorics I, p. 259.
%H A001169 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A001169 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A001169 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Column-ConvexPolyomino.html">Link to a section of The World of Mathematics.</
               a>
%H A001169 D. Zeilberger, <a href="http://arXiv.org/abs/math.CO/9801016">[math/9801016] 
               Automated counting of LEGO towers</a>
%H A001169 <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">Hickerson 
               reference.</a>
%H A001169 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/
               Publications/books.html">Analytic Combinatorics</a>, 2009; see page 
               367
%F A001169 G.f.: x*(1-x)^3/(1-5*x+7*x^2-4*x^3). a(n) = 5a(n-1) - 7a(n-2) + 4a(n-3) 
               for n >= 5.
%p A001169 A001169:=(z-1)**3/(-1+5*z-7*z**2+4*z**3); [Conjectured (correctly) by 
               S. Plouffe in his 1992 dissertation.]
%t A001169 a[ n_ ] := a[ n ]=If[ n<5, {1, 2, 6, 19}[ [ n ] ], 5a[ n-1 ]-7a[ n-2 
               ]+4a[ n-3 ] ].
%Y A001169 a(n) = a(n-1) + A049219(n) + A049220(n) for n >= 2.
%Y A001169 Cf. A049219-A049222.
%Y A001169 Sequence in context: A014346 A118364 A052544 this_sequence A022041 A018906 
               A014010
%Y A001169 Adjacent sequences: A001166 A001167 A001168 this_sequence A001170 A001171 
               A001172
%K A001169 nonn,nice,easy
%O A001169 1,2
%A A001169 N. J. A. Sloane (njas(AT)research.att.com).
%E A001169 More terms from Dean Hickerson (dean.hickerson(AT)yahoo.com)