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%I #5 Mar 31 2012 12:36:30
%S 3,31,212,1317,9499,64832,462515,3316363,23465652,167021811,
%T 1187571067,8438773594,60016633869,426656318067,3033239021542,
%U 21565974491771,153321389406967,1090053687664854,7749841908849879,55097853719155295
%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,3,0,1,0 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 0's, every 3 is next to 3 1's, every 4 is next to 4 0's
%C Column 4 of A197750
%H R. H. Hardin, <a href="/A197746/b197746.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +9*a(n-2) +98*a(n-3) +134*a(n-4) +1211*a(n-5) +1005*a(n-6) +1808*a(n-7) -4815*a(n-8) -24371*a(n-9) -71584*a(n-10) -203938*a(n-11) -431122*a(n-12) -631629*a(n-13) -357858*a(n-14) +1007275*a(n-15) +4113091*a(n-16) +9561411*a(n-17) +22407300*a(n-18) +41834227*a(n-19) +52662256*a(n-20) +53861877*a(n-21) +26436429*a(n-22) -14358629*a(n-23) -122957082*a(n-24) -438504058*a(n-25) -768606468*a(n-26) -775525491*a(n-27) -540471266*a(n-28) -315080489*a(n-29) -31403527*a(n-30) +1061317811*a(n-31) +1974340983*a(n-32) -224751354*a(n-33) -3122610392*a(n-34) -351540051*a(n-35) +6337598809*a(n-36) +3565967257*a(n-37) -11551180391*a(n-38) -19116189238*a(n-39) -3291764167*a(n-40) +20252307776*a(n-41) +20076727482*a(n-42) -3641595935*a(n-43) -18179443352*a(n-44) -6057671898*a(n-45) +10865236692*a(n-46) +8441034605*a(n-47) -3229052082*a(n-48) -5192770670*a(n-49) +91623829*a(n-50) +2636308706*a(n-51) +402165574*a(n-52) -1113858895*a(n-53) -146564753*a(n-54) +475682495*a(n-55) +32453283*a(n-56) -152918585*a(n-57) -4417594*a(n-58) +3521512*a(n-59) -6601819*a(n-60) -8409666*a(n-61) -4134703*a(n-62) +727713*a(n-63) +213604*a(n-64) -21752*a(n-65) +9004*a(n-66) -380*a(n-67) -256*a(n-68)
%e Some solutions containing all values 0 to 4 for n=5
%e ..0..0..0..0....1..3..1..0....0..0..0..0....2..0..0..0....2..0..0..1
%e ..2..0..4..0....0..1..2..0....0..4..0..0....0..4..0..0....0..0..1..3
%e ..1..0..0..1....2..0..0..0....1..0..0..0....0..0..0..1....2..0..0..1
%e ..3..1..1..3....2..0..4..0....3..1..2..0....0..2..1..3....2..0..4..0
%e ..1..0..0..1....0..0..0..0....1..0..2..0....0..2..0..1....0..0..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Oct 17 2011
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