Search: id:A060553
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%I A060553
%S A060553 2,2,4,6,10,16,32,52,104,192,376,720,1440,2800,5600,11072,22112,43968,
%T A060553 87936,175296,350592,700160,1400192,2798336,5596672,11188992,22377984,
%U A060553 44747776,89495040,178973696,357947392,715860992
%N A060553 a(n) is the number of distinct (modulo geometric D3-operations) 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 A060553 A. Barb\'{e}, Symmetric patterns in the cellular automaton that generates 
               Pascal's triangle modulo 2, Discr.Appl.Math. 105(2000),1-38.
%H A060553 Harry J. Smith, <a href="b060553.txt">Table of n, a(n) for n=1,...,500</
               a>
%H A060553 <a href="Sindx_Ce.html#cell">Index entries for sequences related to cellular 
               automata</a>
%F A060553 a(n)={2^(n-1)+2^[floor(n/3) + (n mod 3)mod 2]}/3 + 2^floor[(n-1)/2]
%o A060553 (PARI) { for (n=1, 500, a=(2^(n-1) + 2^(floor(n/3) + (n%3)%2))/3 + 2^floor((n-1)/
               2); write("b060553.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jul 07 2009]
%Y A060553 A060553(n)= [A000079(n-1) + A060547(n)]/3 + A060546(n)/2 A060553(n)= 
               [A000079(n-1) + 2^A008611(n-1)]/3 + 2^[A008619(n-1)-1], for n >= 
               1
%Y A060553 Sequence in context: A084202 A053637 A000016 this_sequence A032307 A007560 
               A032237
%Y A060553 Adjacent sequences: A060550 A060551 A060552 this_sequence A060554 A060555 
               A060556
%K A060553 easy,nonn
%O A060553 1,1
%A A060553 Andr\'{e} Barb\'{e} (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001

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