%I A111340
%S A111340 1,5,51,868
%N A111340 Related to frieze patterns.
%C A111340 The n-th term is the number of positive integer tables a(i,n) (with i 
               running from 1 to n+3 and n running from minus infinity to infinity) 
               subject to the boundary conditions a(i,n) = 0 when i = 1 or i = n+3 
               and a(i,n) = 1 when i = 2 or i = n+2 and the internal condition a(i,
               n-1) a(i,n+1) = a(i-1,n) a(i+1,n) + a(i,n) when i is strictly between 
               2 and n+2.
%C A111340 It is not known as of this writing whether any or all of the terms of 
               the sequence beyond 868 are finite. If the final term "a(i,n)" in 
               the internal condition is replaced by "1", then what we are looking 
               is just a frieze pattern a la Conway and Coxeter (or rather two interlaced 
               frieze patterns that do not interact at all).
%e A111340 The number 1 in the sequence is counting the rather boring configuration
%e A111340 ...
%e A111340 0 1 1 0
%e A111340 0 1 1 0
%e A111340 0 1 1 0
%e A111340 0 1 1 0
%e A111340 0 1 1 0
%e A111340 0 1 1 0
%e A111340 0 1 1 0
%e A111340 0 1 1 0
%e A111340 ...
%e A111340 The number 5 is counting the configuration
%e A111340 ...
%e A111340 0 1 1 1 0
%e A111340 0 1 1 1 0
%e A111340 0 1 2 1 0
%e A111340 0 1 3 1 0
%e A111340 0 1 2 1 0
%e A111340 0 1 1 1 0
%e A111340 0 1 1 1 0
%e A111340 0 1 2 1 0
%e A111340 0 1 3 1 0
%e A111340 0 1 2 1 0
%e A111340 ...
%e A111340 and its four distinct cyclic shifts, each of which repeats with period 
               5
%e A111340 (note the Lyness 5-cycle down the middle).
%Y A111340 Sequence in context: A095839 A107669 A077392 this_sequence A124559 A022516 
               A003515
%Y A111340 Adjacent sequences: A111337 A111338 A111339 this_sequence A111341 A111342 
               A111343
%K A111340 nonn
%O A111340 1,2
%A A111340 N. J. A. Sloane (njas(AT)research.att.com), based on correspondence from 
               James Propp (propp(AT)math.wisc.edu), May 08 2005