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%I #4 Nov 03 2013 06:40:37
%S 0,4,72,1344,20250,375620,6620496,114765278,2040092280,36070020410,
%T 636310267444,11259982687398,199143247111778,3520995724132754,
%U 62277455575772414,1101469857027050006,19480402257921072406
%N Number of nX4 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero
%C Column 4 of A231037
%H R. H. Hardin, <a href="/A231033/b231033.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 21*a(n-1) -43*a(n-2) +423*a(n-3) -14174*a(n-4) +21017*a(n-5) +191825*a(n-6) +94369*a(n-7) -613129*a(n-8) -1029890*a(n-9) -1078481*a(n-10) +5497567*a(n-11) -710152*a(n-12) +3590349*a(n-13) -22983986*a(n-14) +18281674*a(n-15) -13233964*a(n-16) -6664969*a(n-17) +43490862*a(n-18) -17505341*a(n-19) +66788832*a(n-20) -73478356*a(n-21) +1062316*a(n-22) +30795118*a(n-23) -61983450*a(n-24) -3817913*a(n-25) +638020*a(n-26) +8955793*a(n-27) -296821*a(n-28) +286492*a(n-29) +1894901*a(n-30) -851834*a(n-31) +412801*a(n-32) -183119*a(n-33) -7194*a(n-34) +2736*a(n-35) -138*a(n-36) -96*a(n-37)
%e Some solutions for n=3
%e ..0..1..0..1....0..2..2..0....0..1..2..0....0..2..2..0....0..2..2..0
%e ..1..2..2..2....0..1..1..0....2..2..1..1....2..1..1..0....2..1..1..1
%e ..1..0..1..0....0..2..0..2....1..0..0..2....2..0..2..0....2..0..0..2
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 03 2013
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