A222023 - OEIS

A222023

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 1,3,3,1

%I #6 Feb 05 2013 09:20:19

%S 2,3,4,7,11,16,26,42,65,105,168,265,424,675,1070,1707,2715,4315,6875,

%T 10937,17399,27704,44080,70145,111654,177672,282755,450022,716152,

%U 1139735,1813879,2886645,4594007,7311215,11635384,18517300,29469544

%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 1,3,3,1

%C Column 4 of A222027

%H R. H. Hardin, <a href="/A222023/b222023.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +a(n-2) +2*a(n-3) -3*a(n-4) -2*a(n-5) +a(n-6) +3*a(n-7) +2*a(n-8) -5*a(n-9) -2*a(n-10) -a(n-11) +6*a(n-12) +a(n-13) -2*a(n-14) -4*a(n-15) -a(n-16) +4*a(n-17) +2*a(n-18) +3*a(n-19) -6*a(n-20) -3*a(n-21) +9*a(n-23) +2*a(n-24) -6*a(n-25) -5*a(n-26) +8*a(n-28) -a(n-30) -6*a(n-31) -a(n-32) +5*a(n-33) +4*a(n-34) -a(n-35) -6*a(n-36) +7*a(n-38) -2*a(n-39) -6*a(n-40) -4*a(n-41) +8*a(n-42) +2*a(n-43) -5*a(n-44) -2*a(n-45) +3*a(n-46) +4*a(n-47) -3*a(n-48) -a(n-49) +a(n-51)

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

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 05 2013