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%I #17 Jun 13 2015 00:50:26
%S 2,2,4,6,10,16,32,52,104,192,376,720,1440,2800,5600,11072,22112,43968,
%T 87936,175296,350592,700160,1400192,2798336,5596672,11188992,22377984,
%U 44747776,89495040,178973696,357947392,715860992,1431721984,2863378432,5726754816
%N 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.
%H Harry J. Smith, <a href="/A060553/b060553.txt">Table of n, a(n) for n=1..500</a>
%H A. Barbé, <a href="http://dx.doi.org/10.1016/S0166-218X(00)00211-0">Symmetric patterns in the cellular automaton that generates Pascal's triangle modulo 2</a>, Discr. Appl. Math. 105(2000), 1-38.
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-2,-4,-4,8).
%F a(n) = (2^(n-1)+2^(floor(n/3) + (n mod 3)mod 2))/3 + 2^floor((n-1)/2).
%F a(n) = (A000079(n-1) + A060547(n))/3 + A060546(n)/2.
%F a(n) = (A000079(n-1) + 2^A008611(n-1))/3 + 2^(A008619(n-1) - 1), for n >= 1.
%F G.f.: -2*x*(4*x^5 + x^4 - x^3 - 2*x^2 - x + 1) / ((2*x-1)*(2*x^2-1)*(2*x^3-1)). - _Colin Barker_, Aug 29 2013
%o (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); ) } \\ _Harry J. Smith_, Jul 07 2009
%Y Cf. A000079, A060547, A060546, A008611, A008619.
%K easy,nonn
%O 1,1
%A André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001
%E More terms from _Colin Barker_, Aug 29 2013
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