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A206689 Number of nX5 0..3 arrays with no element equal to another within two positions in the same row or column, and new values 0..3 introduced in row major order.

%I A206689 #7 Jul 22 2025 19:36:31
%S A206689 4,116,704,4704,31504,213788,1454810,9933294,67923354,464901756,
%T A206689 3183631874,21807955698,149409637478,1023727198288,7014765000890,
%U A206689 48067928493696,329386094806172,2257144779520590,15467353757059122
%N A206689 Number of nX5 0..3 arrays with no element equal to another within two positions in the same row or column, and new values 0..3 introduced in row major order.
%C A206689 Column 5 of A206692
%H A206689 R. H. Hardin, <a href="/A206689/b206689.txt">Table of n, a(n) for n = 1..210</a>
%F A206689 Empirical: a(n) = 15*a(n-1) -51*a(n-2) -193*a(n-3) +1051*a(n-4) +2372*a(n-5) -12985*a(n-6) -28529*a(n-7) +129318*a(n-8) +212356*a(n-9) -839013*a(n-10) -1225696*a(n-11) +3710749*a(n-12) +5631517*a(n-13) -12635093*a(n-14) -10482155*a(n-15) +20618112*a(n-16) -52448859*a(n-17) +89397201*a(n-18) +475219332*a(n-19) -737964757*a(n-20) -2124354526*a(n-21) +2768115261*a(n-22) +6892655423*a(n-23) -7216788413*a(n-24) -17073837012*a(n-25) +13711465539*a(n-26) +33849631222*a(n-27) -19860441490*a(n-28) -54273123627*a(n-29) +22693872893*a(n-30) +69529238877*a(n-31) -18479245923*a(n-32) -75447262323*a(n-33) +12929746123*a(n-34) +69053543781*a(n-35) -12580606120*a(n-36) -47563475725*a(n-37) +7500075785*a(n-38) +28981491455*a(n-39) -2451216650*a(n-40) -19568112616*a(n-41) +4647832637*a(n-42) +9173909442*a(n-43) -4357897047*a(n-44) -1874621589*a(n-45) +1362472381*a(n-46) +274611989*a(n-47) -277377765*a(n-48) -85579555*a(n-49) +103689018*a(n-50) -6885628*a(n-51) -13682116*a(n-52) +1459344*a(n-53) +585424*a(n-54) +164352*a(n-55) for n>57
%e A206689 Some solutions for n=4
%e A206689 ..0..1..2..0..3....0..1..2..0..1....0..1..2..3..1....0..1..2..0..3
%e A206689 ..2..3..1..2..0....1..3..0..1..3....1..3..0..1..2....1..3..0..1..2
%e A206689 ..1..2..3..1..2....2..0..3..2..0....3..2..1..0..3....2..0..1..2..0
%e A206689 ..0..1..2..0..1....3..1..2..3..1....2..1..3..2..0....3..1..2..0..1
%K A206689 nonn
%O A206689 1,1
%A A206689 _R. H. Hardin_ Feb 11 2012