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A232593 Number of (4+1)X(n+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal.

%I A232593 #6 Jul 23 2025 07:31:32
%S A232593 6,456,122,6406,3002,93236,68072,1364998,1320362,20063788,24123134,
%T A232593 296095446,423016306,4386696696,7216047494,65227876552,120687373030,
%U A232593 973264614932,1988957705626,14569296892014,32409581296990
%N A232593 Number of (4+1)X(n+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal.
%C A232593 Row 4 of A232589
%H A232593 R. H. Hardin, <a href="/A232593/b232593.txt">Table of n, a(n) for n = 1..210</a>
%F A232593 Empirical: a(n) = 20*a(n-2) +16*a(n-3) -92*a(n-4) -260*a(n-5) +82*a(n-6) +1038*a(n-7) +1278*a(n-8) -1350*a(n-9) -4927*a(n-10) -3536*a(n-11) +5500*a(n-12) +12930*a(n-13) +8739*a(n-14) -8650*a(n-15) -22849*a(n-16) -24728*a(n-17) -3836*a(n-18) +33686*a(n-19) +62865*a(n-20) +36392*a(n-21) -44749*a(n-22) -110478*a(n-23) -67221*a(n-24) +47184*a(n-25) +126718*a(n-26) +76044*a(n-27) -30029*a(n-28) -98898*a(n-29) -68985*a(n-30) +2372*a(n-31) +49486*a(n-32) +46722*a(n-33) +19080*a(n-34) -1646*a(n-35) -13297*a(n-36) -15236*a(n-37) -12882*a(n-38) -4684*a(n-39) +949*a(n-40) +3512*a(n-41) +2385*a(n-42) +1194*a(n-43) +233*a(n-44) -6*a(n-45) -67*a(n-46) -18*a(n-47) -2*a(n-48) +2*a(n-49) for n>54
%e A232593 Some solutions for n=5
%e A232593 ..0..1..0..2..1..0....2..1..0..1..2..1....2..1..0..1..2..0....0..1..0..2..1..0
%e A232593 ..2..1..0..2..1..0....2..1..2..1..0..1....0..1..2..0..1..2....2..1..0..2..1..2
%e A232593 ..0..2..1..2..1..2....2..1..2..1..2..1....0..1..2..0..1..2....0..2..1..2..1..0
%e A232593 ..1..0..1..2..1..0....0..1..2..1..0..2....2..0..1..0..1..0....1..0..1..0..1..0
%e A232593 ..1..2..1..0..1..2....2..1..0..2..1..0....1..2..1..2..1..2....1..2..1..2..1..0
%K A232593 nonn
%O A232593 1,1
%A A232593 _R. H. Hardin_, Nov 26 2013