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A231748 Number of nX3 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

%I A231748 #6 Jul 23 2025 06:39:45
%S A231748 9,51,589,5106,41288,397219,3745096,34036486,313782748,2927905037,
%T A231748 27164864918,251564198963,2335778916642,21695352159535,
%U A231748 201366887006680,1869228803618176,17356005419910937,161143681489604094
%N A231748 Number of nX3 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.
%C A231748 Column 3 of A231753
%H A231748 R. H. Hardin, <a href="/A231748/b231748.txt">Table of n, a(n) for n = 1..210</a>
%F A231748 Empirical: a(n) = 9*a(n-1) -10*a(n-2) +205*a(n-3) -343*a(n-4) -3172*a(n-5) -8106*a(n-6) -19608*a(n-7) -86820*a(n-8) +105508*a(n-9) -250613*a(n-10) +525498*a(n-11) +3710627*a(n-12) +6249063*a(n-13) +11770795*a(n-14) -927423*a(n-15) -28037328*a(n-16) -60164511*a(n-17) -139179633*a(n-18) -217274117*a(n-19) -213592727*a(n-20) -140322482*a(n-21) +154891348*a(n-22) +398534065*a(n-23) +772218755*a(n-24) +811574834*a(n-25) +702028305*a(n-26) +477484534*a(n-27) -54847598*a(n-28) -371753704*a(n-29) -646008553*a(n-30) -754680367*a(n-31) -605925622*a(n-32) -423754908*a(n-33) -245157008*a(n-34) -118738252*a(n-35) -48930960*a(n-36) -12367856*a(n-37) -4600192*a(n-38) -2156032*a(n-39) -279552*a(n-40) for n>41
%e A231748 Some solutions for n=5
%e A231748 ..0..0..0....0..1..1....2..0..0....2..0..0....0..0..0....0..0..2....0..1..2
%e A231748 ..1..0..1....0..0..0....2..0..0....0..0..2....0..0..0....1..0..0....0..0..1
%e A231748 ..0..2..2....2..0..0....0..1..1....0..0..2....0..2..2....1..1..0....0..0..2
%e A231748 ..0..0..1....0..0..2....0..0..1....0..0..1....2..0..2....2..0..2....2..0..1
%e A231748 ..2..0..0....0..1..1....0..0..1....1..0..0....0..0..0....0..0..0....0..0..0
%K A231748 nonn
%O A231748 1,1
%A A231748 _R. H. Hardin_, Nov 13 2013