%I A060552
%S A060552 0,0,0,1,2,7,14,35,70,154,310,650,1300,2666,5332,10788,21588,43428,
%T A060552 86856,174244,348488,697992,1396040,2794120,5588240,11180680,22361360,
%U A060552 44730896,89462032,178940432,357880864,715794960
%N A060552 a(n) is the number of distinct (modulo geometric D3-operations) nonsymmetric 
               (no reflective nor rotational symmetry) patterns which can be formed 
               by an 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 A060552 A. Barb\'{e}, Symmetric patterns in the cellular automaton that generates 
               Pascal's triangle modulo 2, Discr. Appl. Math. 105(2000), 1-38.
%H A060552 Harry J. Smith, <a href="b060552.txt">Table of n, a(n) for n=1,...,500</
               a>
%H A060552 <a href="Sindx_Ce.html#cell">Index entries for sequences related to cellular 
               automata</a>
%F A060552 a(n)={2^(n-1)-2^[floor(n/3)+(n mod 3)mod 2-1]}/3+2^{floor[(n+3)/6]+d(n)-1} 
               -2^floor[(n-1)/2], with d(n)=1 if n mod 6=1 else d(n)=0.
%F A060552 Contribution from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 03 
               2009: (Start)
%F A060552 a(n)= 2*a(n-1) +2*a(n-2) -2*a(n-3) -4*a(n-4) -4*a(n-5) +10*a(n-6) -4*a(n-7) 
               -4*a(n-8) +4*a(n-9) +8*a(n-10) +8*a(n-11) -16*a(n-12).
%F A060552 G.f.: -x^4*(-1-x^2-x^4+2*x^3+2*x^5+2*x^6)/((2*x-1)*(2*x^2-1)*(2*x^3-1)*(2*x^6-1)). 
               (End)
%o A060552 (PARI) { for (n=1, 500, a=(2^(n-1)-2^(floor(n/3)+(n%3)%2-1))/3+2^(floor((n+3)/
               6)+(n%6==1)-1)-2^floor((n-1)/2); write("b060552.txt", n, " ", a); 
               ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 07 2009]
%Y A060552 A060552(n)=[A000079(n-1) - A060547(n)/2]/3 + A060548(n)/2 -A060546(n)/
               2 A060552(n)={A000079(n-1) - 2^[A008611(n-1)-1]}/3+ 2^[A008615(n+1)-1] 
               -2^[A008619(n-1)-1], n >= 1
%Y A060552 Sequence in context: A018453 A000147 A128902 this_sequence A167762 A018497 
               A107373
%Y A060552 Adjacent sequences: A060549 A060550 A060551 this_sequence A060553 A060554 
               A060555
%K A060552 easy,nonn
%O A060552 1,5
%A A060552 Andr\'{e} Barb\'{e} (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001