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%I #5 Mar 31 2012 12:36:25
%S 5,57,299,2223,16949,119487,869434,6327405,45825170,332648911,
%T 2414803873,17522373803,127164315152,922879040046,6697507656945,
%U 48605408464469,352741515035141,2559929316113824,18578023371928916,134825191242742049
%N Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,4,0,2,3 for x=0,1,2,3,4
%C Every 0 is next to 0 1's, every 1 is next to 1 4's, every 2 is next to 2 0's, every 3 is next to 3 2's, every 4 is next to 4 3's
%C Column 5 of A196343
%H R. H. Hardin, <a href="/A196340/b196340.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 5*a(n-1) +8*a(n-2) +42*a(n-3) +116*a(n-4) +45*a(n-5) +895*a(n-6) -315*a(n-7) -1358*a(n-8) -17019*a(n-9) -61913*a(n-10) +18538*a(n-11) -48426*a(n-12) -344003*a(n-13) +1184845*a(n-14) +3828333*a(n-15) +599626*a(n-16) -7167543*a(n-17) -4621582*a(n-18) +584889*a(n-19) -30485068*a(n-20) -70025284*a(n-21) -7991285*a(n-22) +194398049*a(n-23) +374666400*a(n-24) +218790373*a(n-25) -9116757*a(n-26) +72577759*a(n-27) +71107276*a(n-28) -738985322*a(n-29) -1775222937*a(n-30) -1369022818*a(n-31) +429068913*a(n-32) +1892447203*a(n-33) +1717602454*a(n-34) +1004647670*a(n-35) -239036570*a(n-36) -1779459899*a(n-37) -2813513971*a(n-38) -2536913821*a(n-39) -537173362*a(n-40) +2567388282*a(n-41) +5019655793*a(n-42) +4972780323*a(n-43) +1300345327*a(n-44) -3785463308*a(n-45) -5511670674*a(n-46) -3329819222*a(n-47) +1542046077*a(n-48) +4185764391*a(n-49) +3366883513*a(n-50) +66662821*a(n-51) -1541326483*a(n-52) -1796928920*a(n-53) -395298815*a(n-54) +648560821*a(n-55) +735751251*a(n-56) +128410953*a(n-57) -621249729*a(n-58) -758316818*a(n-59) -256023615*a(n-60) +162970616*a(n-61) +204547296*a(n-62) +8148040*a(n-63) -132750984*a(n-64) +12369634*a(n-65) +48202308*a(n-66) +18304099*a(n-67) -9767424*a(n-68) -14852803*a(n-69) -489702*a(n-70) -467359*a(n-71) -3057058*a(n-72) -785431*a(n-73) +953186*a(n-74) +703957*a(n-75) +77119*a(n-76) -9802*a(n-77) -8932*a(n-78) -26827*a(n-79) -3993*a(n-80) +1558*a(n-81) -459*a(n-82) +172*a(n-83) +108*a(n-84) -12*a(n-85)
%e Some solutions for n=4
%e ..0..0..0..0..2....0..2..2..0..0....0..0..2..2..0....2..0..0..0..0
%e ..0..0..0..0..0....0..0..0..0..0....2..2..0..0..0....0..0..0..0..0
%e ..0..0..0..0..0....0..0..0..0..0....0..2..0..0..0....0..2..2..2..0
%e ..2..0..0..0..0....2..0..2..2..0....0..2..0..0..2....0..2..0..2..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Oct 01 2011
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