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Number of 4Xn 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero
1

%I #4 Nov 06 2013 05:43:38

%S 0,20,552,5992,76264,1081934,15270416,213355654,2979297186,

%T 41637993524,582001470148,8134516660856,113692450572670,

%U 1589033640398564,22209327313491742,310411398997352946,4338502347339782972

%N Number of 4Xn 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero

%C Row 4 of A231246

%H R. H. Hardin, <a href="/A231249/b231249.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 15*a(n-1) -25*a(n-2) +148*a(n-3) +122*a(n-4) -1205*a(n-5) -2750*a(n-6) -2119*a(n-7) +1020*a(n-8) +18937*a(n-9) +50454*a(n-10) +61769*a(n-11) -6359*a(n-12) -151941*a(n-13) -166619*a(n-14) +30896*a(n-15) +129574*a(n-16) +38876*a(n-17) -30440*a(n-18) -29584*a(n-19) -9952*a(n-20) +1728*a(n-21) +1280*a(n-22) for n>23

%e Some solutions for n=4

%e ..0..3..0..3....0..3..2..1....0..1..0..1....0..1..2..3....0..3..2..1

%e ..2..1..2..1....0..1..2..3....2..1..2..1....0..1..0..1....2..1..0..3

%e ..2..3..0..3....0..3..0..3....0..3..0..3....0..3..0..3....0..1..0..3

%e ..0..1..2..3....2..1..0..3....2..1..0..3....0..1..2..1....0..1..2..1

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 06 2013