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%I #5 Mar 31 2012 12:36:30
%S 3,19,24,131,206,834,2081,6653,15931,48796,135249,391078,1061878,
%T 3054971,8582689,24243393,67728862,192162581,541573358,1525969004,
%U 4291400929,12116692925,34147187837,96210697228,271054147869,764411232314
%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,2,1,1,1 for x=0,1,2,3,4
%C Every 0 is next to 0 2's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's
%C Column 4 of A197545
%H R. H. Hardin, <a href="/A197541/b197541.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +7*a(n-2) -14*a(n-3) -7*a(n-4) +40*a(n-5) -27*a(n-6) +27*a(n-7) +109*a(n-8) -1131*a(n-9) -682*a(n-10) +5832*a(n-11) -302*a(n-12) -15793*a(n-13) +10796*a(n-14) +26552*a(n-15) -9592*a(n-16) -54794*a(n-17) -65338*a(n-18) +161498*a(n-19) +192943*a(n-20) -209955*a(n-21) -329504*a(n-22) -35891*a(n-23) +626888*a(n-24) +8303*a(n-25) -624179*a(n-26) +346017*a(n-27) -201978*a(n-28) +897796*a(n-29) -654490*a(n-30) -1864676*a(n-31) +3767465*a(n-32) -1840154*a(n-33) -2178898*a(n-34) +4365803*a(n-35) -4227708*a(n-36) +1275734*a(n-37) +763034*a(n-38) -2336201*a(n-39) +2085583*a(n-40) +113233*a(n-41) -1187876*a(n-42) -428063*a(n-43) +2589233*a(n-44) -1866000*a(n-45) -489531*a(n-46) +1622870*a(n-47) -892532*a(n-48) +155171*a(n-49) -471*a(n-50) -1098*a(n-51)
%e Some solutions containing all values 0 to 4 for n=5
%e ..0..1..2..1....2..1..3..1....1..0..1..2....0..1..2..1....0..1..2..1
%e ..1..3..2..1....1..4..1..2....2..1..4..1....1..3..2..1....1..3..2..1
%e ..2..1..1..3....3..1..1..2....2..1..1..3....2..1..1..0....2..1..1..3
%e ..2..1..4..1....1..2..3..1....1..3..2..1....2..1..4..1....2..1..4..1
%e ..1..3..1..2....1..2..1..0....0..1..2..1....1..0..1..2....1..0..1..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Oct 16 2011
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