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Number of nX3 0..3 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..3 introduced in row major order
1

%I #4 Apr 12 2014 15:45:05

%S 2,28,475,8319,147231,2610234,46306024,821735065,14584690111,

%T 258881423308,4595421744553,81575772171285,1448115454676354,

%U 25706831513670064,456347578032510469,8101099194201232529

%N Number of nX3 0..3 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..3 introduced in row major order

%C Column 3 of A240774

%H R. H. Hardin, <a href="/A240771/b240771.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 37*a(n-1) -470*a(n-2) +2696*a(n-3) -8168*a(n-4) +13440*a(n-5) -3283*a(n-6) -17901*a(n-7) +16963*a(n-8) -662153*a(n-9) +2664795*a(n-10) -3360533*a(n-11) +5535617*a(n-12) -10243067*a(n-13) +6443530*a(n-14) -26560330*a(n-15) +17640820*a(n-16) -2905958*a(n-17) +97439023*a(n-18) +42291829*a(n-19) +35730762*a(n-20) -151787048*a(n-21) -158957051*a(n-22) -133982717*a(n-23) +87202313*a(n-24) +159399645*a(n-25) +153736110*a(n-26) +5561244*a(n-27) -76184253*a(n-28) -59257575*a(n-29) -14782176*a(n-30) +18219168*a(n-31) +9065115*a(n-32) -1423737*a(n-33) -826686*a(n-34) for n>35

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2014