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A202882 Number of n X 1 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

%I A202882 #16 Jul 18 2023 11:21:38
%S A202882 1,3,9,22,51,121,292,704,1691,4059,9749,23422,56268,135166,324692,
%T A202882 779977,1873673,4500958,10812237,25973244,62393157,149881402,
%U A202882 360046432,864906711,2077686532,4991036946,11989513056,28801314179,69186771332
%N A202882 Number of n X 1 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.
%H A202882 R. H. Hardin, <a href="/A202882/b202882.txt">Table of n, a(n) for n = 1..210</a>
%H A202882 T. Mansour and M. Shattuck, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Shattuck/shattuck3.html">Counting Peaks and Valleys in a Partition of a Set</a>, J. Int. Seq. 13 (2010), 10.6.8, Lemma 2.1, k=3, one peak.
%F A202882 Empirical: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5).
%F A202882 Empirical: G.f.: -x*(1+3*x^2+x^4)/(-1+3*x-3*x^2+4*x^3-x^4+x^5). - _R. J. Mathar_, Jul 09 2017
%e A202882 Some solutions for n=5
%e A202882 ..2....2....1....0....2....2....0....1....0....1....1....0....2....1....0....2
%e A202882 ..2....2....1....1....2....2....2....1....2....2....1....0....2....2....1....2
%e A202882 ..0....1....1....2....0....2....2....0....2....2....1....1....1....2....1....0
%e A202882 ..0....1....1....2....1....1....2....0....0....0....2....1....2....2....2....2
%e A202882 ..0....0....1....2....1....1....1....0....0....0....2....1....2....0....2....2
%Y A202882 Column 1 of A202889.
%K A202882 nonn
%O A202882 1,2
%A A202882 _R. H. Hardin_, Dec 25 2011