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A240890 Number of nX5 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

%I A240890 #6 Jul 23 2025 11:08:04
%S A240890 8,116,1485,19065,245268,3146755,40424861,519218802,6669141957,
%T A240890 85661208693,1100266812500,14132294288479,181521187277681,
%U A240890 2331535718787322,29947240904675409,384655164983132569
%N A240890 Number of nX5 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.
%C A240890 Column 5 of A240893
%H A240890 R. H. Hardin, <a href="/A240890/b240890.txt">Table of n, a(n) for n = 1..210</a>
%F A240890 Empirical: a(n) = 16*a(n-1) -22*a(n-2) -276*a(n-3) +543*a(n-4) +1114*a(n-5) -24150*a(n-6) -6509*a(n-7) +197916*a(n-8) +80150*a(n-9) -592045*a(n-10) +4684412*a(n-11) +15106341*a(n-12) -17190009*a(n-13) -90244020*a(n-14) -91211136*a(n-15) -290130772*a(n-16) -407134336*a(n-17) +671095240*a(n-18) +2173631712*a(n-19) +6313455104*a(n-20) +12278947872*a(n-21) +8033752064*a(n-22) +6113760384*a(n-23) -31674604288*a(n-24) -122704805888*a(n-25) -110531544064*a(n-26) -270879311872*a(n-27) -593695940608*a(n-28) +82971942912*a(n-29) +283392655360*a(n-30) -69979668480*a(n-31) +3328745078784*a(n-32) +4282541146112*a(n-33) +2076075098112*a(n-34) +9789286383616*a(n-35) +7759030386688*a(n-36) +1140229931008*a(n-37) +7107835330560*a(n-38) -2054940524544*a(n-39) -10791105331200*a(n-40) -2076616687616*a(n-41) -14566381584384*a(n-42) -20598663151616*a(n-43) -2336462209024*a(n-44) -13056700579840*a(n-45) -3848290697216*a(n-46) +3298534883328*a(n-47) -4398046511104*a(n-48)
%e A240890 Some solutions for n=4
%e A240890 ..0..1..2..1..0....0..1..1..2..0....0..1..1..2..0....0..1..2..1..2
%e A240890 ..1..0..1..2..1....1..1..1..1..2....2..1..1..0..2....1..2..1..0..1
%e A240890 ..2..1..0..1..0....1..1..1..1..0....1..0..0..1..0....2..1..0..2..2
%e A240890 ..0..2..1..0..2....2..1..1..0..1....2..0..0..2..1....1..0..1..2..2
%K A240890 nonn
%O A240890 1,1
%A A240890 _R. H. Hardin_, Apr 14 2014