A222123 - OEIS

%I #9 Aug 15 2018 12:38:13

%S 2,3,4,8,12,19,31,48,79,126,200,322,513,823,1318,2105,3372,5394,8632,

%T 13817,22103,35374,56607,90580,144956,231952,371177,593973,950478,

%U 1520987,2433908,3894788,6232544,9973435,15959719,25539092,40868195

%N Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..4 array extended with zeros and convolved with 1,2,1.

%C Column 4 of A222127.

%H R. H. Hardin, <a href="/A222123/b222123.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + a(n-3) + 2*a(n-5) - a(n-6).

%F Empirical g.f.: x*(2 + x + x^2 + 2*x^3 + x^4 - x^5) / (1 - x - x^3 - 2*x^5 + x^6). - _Colin Barker_, Aug 15 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....1....0....1....0....0....0....0....0....0....0....0....0....1....1

%e ..1....1....0....0....0....1....0....1....1....0....1....0....1....0....0....0

%e ..0....0....0....1....1....0....0....0....0....0....0....1....0....0....0....0

%e ..0....1....1....0....0....1....0....0....0....0....0....0....1....1....0....1

%e ..1....0....0....0....0....0....1....0....0....0....1....0....0....0....0....0

%e ..0....0....0....0....0....0....0....1....0....0....0....1....1....1....0....0

%e ..1....1....1....0....1....0....0....0....1....0....0....0....0....0....1....0

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%Y Cf. A222127.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 08 2013