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%I #5 Mar 31 2012 12:36:29
%S 1,17,83,441,2289,12399,71411,387651,2116197,11718977,64938109,
%T 356963085,1965892155,10861424867,59918428781,330197022079,
%U 1821334406081,10048722879503,55415859459949,305604003423219,1685661404741659
%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,3,1,1,0 for x=0,1,2,3,4
%C Every 0 is next to 0 3's, every 1 is next to 1 3's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 0's
%C Column 4 of A197350
%H R. H. Hardin, <a href="/A197346/b197346.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +17*a(n-2) +51*a(n-3) +116*a(n-4) -1173*a(n-5) -4317*a(n-6) -2422*a(n-7) +14592*a(n-8) +119209*a(n-9) +264265*a(n-10) -221880*a(n-11) -1447910*a(n-12) -4035783*a(n-13) -7712675*a(n-14) +11905429*a(n-15) +52724270*a(n-16) +55553686*a(n-17) +111373104*a(n-18) -149159569*a(n-19) -967541103*a(n-20) -292339605*a(n-21) -714338479*a(n-22) -752792361*a(n-23) +9858752342*a(n-24) +1954128572*a(n-25) +1809533199*a(n-26) +24179073120*a(n-27) -66790076576*a(n-28) -24201485912*a(n-29) +11589593240*a(n-30) -167312714112*a(n-31) +273578008400*a(n-32) +149893236208*a(n-33) -15833303632*a(n-34) +447963794496*a(n-35) -654166650816*a(n-36) -405019304448*a(n-37) -108774022144*a(n-38) -67371539456*a(n-39) +217477283840*a(n-40) +393793961984*a(n-41) +183423074304*a(n-42) -46152155136*a(n-43) -33077329920*a(n-44) -3397386240*a(n-45)
%e Some solutions containing all values 0 to 4 for n=5
%e ..0..0..0..0....0..1..3..1....1..2..0..0....0..0..0..0....0..0..2..1
%e ..0..0..4..0....0..0..1..0....3..1..0..1....0..4..0..0....0..0..1..3
%e ..0..0..0..0....0..4..0..0....1..0..1..3....0..0..0..0....0..0..2..1
%e ..0..0..1..2....0..0..1..2....0..4..0..1....2..1..0..0....0..4..0..0
%e ..0..1..3..1....0..1..3..1....0..0..0..0....1..3..1..0....0..0..0..0
%K nonn
%O 1,2
%A _R. H. Hardin_ Oct 13 2011
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