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%I #5 Mar 31 2012 12:36:27
%S 4,48,562,5465,58639,634241,6764386,72281541,773637307,8274218119,
%T 88495136248,946584068019,10124647473535,108293363518701,
%U 1158313188626715,12389366140294426,132517210297246830
%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,1,2,0,3 for x=0,1,2,3,4
%C Every 0 is next to 0 4's, every 1 is next to 1 1's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 3's
%C Column 4 of A196967
%H R. H. Hardin, <a href="/A196963/b196963.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 6*a(n-1) +28*a(n-2) +243*a(n-3) +129*a(n-4) -627*a(n-5) -11946*a(n-6) -24716*a(n-7) -41353*a(n-8) +176819*a(n-9) +180212*a(n-10) +7668*a(n-11) +622543*a(n-12) +553736*a(n-13) +3854835*a(n-14) -3424516*a(n-15) +2196679*a(n-16) -13381328*a(n-17) +10523502*a(n-18) +49130245*a(n-19) -8284473*a(n-20) -43391724*a(n-21) -177460574*a(n-22) +198448096*a(n-23) -92523963*a(n-24) -4740245*a(n-25) -228506537*a(n-26) -172761713*a(n-27) +880385660*a(n-28) -173687712*a(n-29) -584399710*a(n-30) -1963152979*a(n-31) +3777292865*a(n-32) -1265968818*a(n-33) -7515820754*a(n-34) +5194885668*a(n-35) +20885154295*a(n-36) -2530524728*a(n-37) -39211330906*a(n-38) -3415305019*a(n-39) +47680035982*a(n-40) +22891413623*a(n-41) -62265733702*a(n-42) -38098494791*a(n-43) +55080130009*a(n-44) +61886139498*a(n-45) -39779711776*a(n-46) -58974614190*a(n-47) +14662698157*a(n-48) +38116570688*a(n-49) +5276636734*a(n-50) -24203947887*a(n-51) -10142236375*a(n-52) -1836219594*a(n-53) +9910595092*a(n-54) +27385297940*a(n-55) +8628758094*a(n-56) -32441265689*a(n-57) -23930856404*a(n-58) +15630720154*a(n-59) +20769255077*a(n-60) +270173720*a(n-61) -12293398785*a(n-62) +446073911*a(n-63) +2918441286*a(n-64) -1979814862*a(n-65) +185646866*a(n-66) +973888331*a(n-67) +512852806*a(n-68) -960049045*a(n-69) +76723459*a(n-70) +239033946*a(n-71) -128970197*a(n-72) +50836450*a(n-73) -5269426*a(n-74) +33947945*a(n-75) -44325642*a(n-76) +699720*a(n-77) +10696312*a(n-78) -894914*a(n-79) -686021*a(n-80) -1449584*a(n-81) +1440552*a(n-82) -203671*a(n-83) -120512*a(n-84) +35987*a(n-85) -5446*a(n-86) +12425*a(n-87) -14819*a(n-88) +1800*a(n-89) +1710*a(n-90) -238*a(n-91) -36*a(n-92)
%e Some solutions for n=5
%e ..0..0..3..0....1..1..0..0....0..0..2..2....0..0..0..0....1..1..0..0
%e ..0..0..0..0....0..0..2..2....1..0..2..2....3..0..0..1....0..0..2..2
%e ..1..1..0..3....1..0..2..2....1..3..0..0....0..3..0..1....0..0..2..2
%e ..2..2..0..0....1..0..3..0....0..0..0..3....1..2..2..0....0..0..1..0
%e ..2..2..0..0....0..0..0..0....0..3..0..0....1..2..2..0....0..0..1..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Oct 08 2011
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