A222021 - OEIS

A222021

Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,3,3,1.

%I #13 Aug 14 2018 21:03:41

%S 2,3,4,6,10,15,23,36,55,84,129,198,303,465,714,1095,1680,2578,3955,

%T 6067,9308,14280,21907,33609,51562,79104,121358,186183,285634,438207,

%U 672279,1031382,1582302,2427501,3724170,5713464,8765355,13447438,20630491

%N Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,3,3,1.

%C Column 2 of A222027.

%H R. H. Hardin, <a href="/A222021/b222021.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + a(n-3) + a(n-7) + a(n-9).

%F Empirical g.f.: x*(2 + x + x^2 + x^4 + x^5 + 2*x^6 + x^7 + x^8) / ((1 - x + x^2 - x^3 + x^4)*(1 - x^2 - x^3 - x^4 - x^5)). - _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....1....0....0....0....1....0....1....0....0....0....0....1

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

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

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

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

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

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

%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