A222105 - OEIS

A222105

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 1,2,2,1.

%I #7 Dec 30 2023 21:43:20

%S 2,3,4,5,8,12,17,24,36,53,76,109,161,236,342,498,729,1064,1545,2256,

%T 3296,4807,7004,10220,14915,21744,31715,46271,67503,98445,143596,

%U 209477,305548,445679,650102,948313,1383244,2017670,2943130,4293056,6262110

%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 1,2,2,1.

%C Column 2 of A222111.

%H R. H. Hardin, <a href="/A222105/b222105.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +a(n-4) +4*a(n-7) -3*a(n-8) -2*a(n-11) -5*a(n-14) +3*a(n-15) +a(n-18) +2*a(n-21) -a(n-22).

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

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

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

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

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

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

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

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

%Y Cf. A222111.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 07 2013