cp's OEIS Frontend

A203175 Number of nX2 0..2 arrays with every 1 immediately preceded by 0 to the left or above, no 0 immediately preceded by a 0, and every 2 immediately preceded by 0 1 to the left or above.

%I A203175 #28 Jul 29 2024 06:17:42
%S A203175 1,1,2,4,6,10,18,30,50,86,146,246,418,710,1202,2038,3458,5862,9938,
%T A203175 16854,28578,48454,82162,139318,236226,400550,679186,1151638,1952738,
%U A203175 3311110,5614386,9519862,16142082,27370854,46410578,78694742,133436450,226257606
%N A203175 Number of nX2 0..2 arrays with every 1 immediately preceded by 0 to the left or above, no 0 immediately preceded by a 0, and every 2 immediately preceded by 0 1 to the left or above.
%C A203175 Column 2 of A203181.
%C A203175 It seems that for n>=1 a(n) equals the number of (n-1)-length binary words avoiding runs of zeros of length 1 (mod 3). - _Milan Janjic_, Feb 28 2015
%D A203175 D. E. Daykin and S. J. Tucker, Introduction to Dragon Curves. Unpublished, 1976. See links in A003229 for an earlier version. See beta_n for this sequence. - _N. J. A. Sloane_, Jul 08 2014
%H A203175 R. H. Hardin, <a href="/A203175/b203175.txt">Table of n, a(n) for n = 1..210</a>
%H A203175 Matthias Beck and Neville Robbins, <a href="http://arxiv.org/abs/1403.0665">Variations on a Generatingfunctional Theme: Enumerating Compositions with Parts Avoiding an Arithmetic Sequence</a>, arXiv:1403.0665 [math.NT], 2014.
%H A203175 Helena Verrill, <a href="https://arxiv.org/abs/2407.17326">On the Boundary of the Harter-Heighway dragon curve</a>, arXiv:2407.17326 [math.CO], 2024.
%F A203175 Empirical: a(n) = a(n-1) + 2*a(n-3) = A003229(n-4)+A003229(n-2).
%F A203175 Empirical G.f.: -x*(1+x^2) / ( -1+x+2*x^3 ). - _R. J. Mathar_, Jul 02 2013
%e A203175 All solutions for n=5:
%e A203175 ..0..1....0..1....0..1....0..1....0..1....0..1
%e A203175 ..1..0....1..0....1..0....1..0....1..0....1..0
%e A203175 ..0..1....0..1....0..1....2..1....2..1....0..1
%e A203175 ..1..0....1..2....1..0....0..1....0..2....1..2
%e A203175 ..2..1....2..0....0..1....1..0....1..0....0..1
%Y A203175 Cf. A003229, A203181.
%K A203175 nonn
%O A203175 1,3
%A A203175 _R. H. Hardin_, Dec 30 2011