%I #10 Aug 14 2018 21:03:48
%S 2,3,4,7,11,16,26,41,62,99,156,242,382,600,938,1475,2314,3627,5696,
%T 8935,14016,22000,34515,54153,84981,133334,209209,328278,515083,
%U 808208,1268156,1989823,3122203,4899001,7686907,12061403,18925330,29695352
%N Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..3 array extended with zeros and convolved with 1,3,3,1.
%C Column 3 of A222027.
%H R. H. Hardin, <a href="/A222022/b222022.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 2*a(n-3) - a(n-4) + a(n-8) - a(n-9) + a(n-11) - a(n-12) - 2*a(n-14) + a(n-15).
%F Empirical g.f.: x*(2 + x + x^2 - x^3 - 2*x^8 - 2*x^11 - x^12 - x^13 + x^14) / ((1 - x)*(1 + x + x^2)*(1 - x - x^3 - x^6 - x^8 - 2*x^11 + x^12)). - _Colin Barker_, Aug 14 2018
%e Some solutions for n=7, one extended zero followed by filtered positions:
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....1....0....0....0....1....1....0....1....0....1....0....1....0....0....1
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....1....1....0
%e ..0....1....0....0....1....0....1....0....0....0....0....1....0....0....0....1
%e ..0....0....1....1....0....1....0....0....0....0....1....0....0....1....0....0
%e ..1....0....0....0....1....0....0....1....0....0....0....0....0....0....0....0
%e ..0....0....1....0....0....1....1....0....0....0....0....0....1....0....0....0
%e ..0....1....0....0....0....0....0....0....0....0....1....1....0....0....1....0
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%Y Cf. A222027.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2013