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A203096 Number of nX3 0..3 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

%I A203096 #7 Jul 22 2025 17:01:29
%S A203096 16,1080,48552,2029744,87531478,3790420430,163621176194,7062389921398,
%T A203096 304924052795176,13165093367601574,568388578666214512,
%U A203096 24539653368720439680,1059478958509288348530,45742091639005479963848
%N A203096 Number of nX3 0..3 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.
%C A203096 Column 3 of A203101
%H A203096 R. H. Hardin, <a href="/A203096/b203096.txt">Table of n, a(n) for n = 1..210</a>
%F A203096 Empirical: a(n) = 50*a(n-1) -535*a(n-2) +11739*a(n-3) -81311*a(n-4) +952118*a(n-5) +111609*a(n-6) +23983533*a(n-7) -3575174*a(n-8) -48024160*a(n-9) -3036762623*a(n-10) -9698998582*a(n-11) -75254884745*a(n-12) -75786404331*a(n-13) +371496113408*a(n-14) +937086665510*a(n-15) +4071380170270*a(n-16) +3207519674660*a(n-17) -35547187154396*a(n-18) -50104627883832*a(n-19) +46707082317648*a(n-20) +99704384719248*a(n-21) +189399657391776*a(n-22) +190022854545216*a(n-23) -666178095939264*a(n-24) -983552499278784*a(n-25) +737232848225280*a(n-26) +1440464494146048*a(n-27) -239620376715264*a(n-28) -944613888076800*a(n-29) -83452415201280*a(n-30) +280410806292480*a(n-31) +62187583832064*a(n-32) -30045400989696*a(n-33) -8916100448256*a(n-34)
%e A203096 Some solutions for n=5
%e A203096 ..1..0..0....2..1..0....1..3..0....0..0..3....1..2..1....1..1..1....0..3..3
%e A203096 ..3..2..1....3..3..3....0..3..2....0..1..3....3..2..0....2..2..3....2..3..1
%e A203096 ..3..3..3....3..3..2....0..1..2....2..0..2....3..2..2....0..3..3....1..0..3
%e A203096 ..3..3..0....1..3..1....0..1..1....2..1..0....0..1..0....0..0..3....2..1..3
%e A203096 ..1..1..1....3..3..0....2..3..3....3..3..2....0..1..0....3..3..2....2..3..3
%K A203096 nonn
%O A203096 1,1
%A A203096 _R. H. Hardin_ Dec 29 2011