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A238318 Number of (n+1)X(3+1) 0..2 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors.

%I A238318 #6 Jul 23 2025 10:51:43
%S A238318 22,376,4294,41046,405636,4245918,44773061,466364332,4831077908,
%T A238318 50118953924,520906788265,5414918911420,56265498867083,
%U A238318 584547225602293,6073257215133643,63102941239457036,655660370108720902
%N A238318 Number of (n+1)X(3+1) 0..2 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors.
%C A238318 Column 3 of A238323
%H A238318 R. H. Hardin, <a href="/A238318/b238318.txt">Table of n, a(n) for n = 1..210</a>
%F A238318 Empirical: a(n) = 14*a(n-1) -69*a(n-2) +338*a(n-3) -119*a(n-4) -205*a(n-5) +3136*a(n-6) +585*a(n-7) -35422*a(n-8) +20437*a(n-9) +61393*a(n-10) -336471*a(n-11) -66762*a(n-12) +1255786*a(n-13) -168329*a(n-14) -1982021*a(n-15) +2418579*a(n-16) +2176189*a(n-17) -8355481*a(n-18) -4601562*a(n-19) +12549690*a(n-20) +7969403*a(n-21) -9569735*a(n-22) -6645703*a(n-23) +4296381*a(n-24) +2341505*a(n-25) -1782000*a(n-26) -206421*a(n-27) +727746*a(n-28) -138501*a(n-29) -247543*a(n-30) +28937*a(n-31) +27566*a(n-32) -3059*a(n-33) +13415*a(n-34) +6590*a(n-35) -2745*a(n-36) -793*a(n-37) +610*a(n-38) +103*a(n-39) -62*a(n-40) -17*a(n-41) +a(n-42) +a(n-43)
%e A238318 Some solutions for n=4
%e A238318 ..2..2..0..0....2..2..2..0....2..2..2..1....2..2..2..2....1..1..0..0
%e A238318 ..1..1..0..0....2..2..1..0....1..1..0..0....0..2..2..2....1..1..0..0
%e A238318 ..0..1..1..1....2..2..1..1....0..0..0..0....0..1..1..0....2..2..0..0
%e A238318 ..0..2..2..0....2..2..2..0....0..0..1..1....0..1..1..0....2..2..2..1
%e A238318 ..2..2..2..0....2..2..2..0....1..1..1..1....0..1..1..1....2..2..2..2
%K A238318 nonn
%O A238318 1,1
%A A238318 _R. H. Hardin_, Feb 24 2014