%I A060546
%S A060546 2,2,4,4,8,8,16,16,32,32,64,64,128,128,256,256,512,512,1024,1024,2048,
%T A060546 2048,4096,4096,8192,8192,16384,16384,32768,32768,65536,65536,131072,
%U A060546 131072,262144,262144,524288,524288,1048576,1048576,2097152,2097152
%N A060546 a(n) is the number of median-reflective (palindrome) symmetric patterns 
               in a top-down equilateral triangular arrangement of closely packed 
               black and white cells satisfying the local matching rule of Pascal's 
               triangle modulo 2, where n is the number of cells in each edge of 
               the arrangement. The matching rule is such that any elementary top-down 
               triangle of three neighboring cells in the arrangement contains either 
               one or three white cells.
%D A060546 A. Barb\'{e}, Symmetric patterns in the cellular automaton that generates 
               Pascal's triangle modulo 2, Discr. Appl. Math. 105(2000), 1-38.
%H A060546 Harry J. Smith, <a href="b060546.txt">Table of n, a(n) for n=1,...,500</
               a>
%H A060546 <a href="Sindx_Ce.html#cell">Index entries for sequences related to cellular 
               automata</a>
%F A060546 a(n) =2^ceil(n/2)
%p A060546 for n from 1 to 100 do printf(`%d,`,2^ceil(n/2)) od:
%o A060546 (PARI) { for (n=1, 500, write("b060546.txt", n, " ", 2^ceil(n/2)); ) 
               } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 06 2009]
%Y A060546 a(n)=A016116(n+1) for n >= 1 a(n)=2^A008619(n-1) for n >= 1
%Y A060546 Sequence in context: A117575 A152166 A016116 this_sequence A163403 A120803 
               A000011
%Y A060546 Adjacent sequences: A060543 A060544 A060545 this_sequence A060547 A060548 
               A060549
%K A060546 easy,nice,nonn
%O A060546 1,1
%A A060546 Andr\'{e} Barb\'{e} (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001
%E A060546 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 04 2001