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Number of (n+1)X5 0..3 arrays containing all values 0..3 with every 2X2 subblock having one or two distinct values, and new values 0..3 introduced in row major order
1

%I #5 Mar 31 2012 12:37:31

%S 162,13529,870686,53890394,3143493049,176163769267,9585247795332,

%T 510324389383430,26728547640264511,1382481145423604439,

%U 70813668245584753816,3599637037473025226780,181875667113421394973161

%N Number of (n+1)X5 0..3 arrays containing all values 0..3 with every 2X2 subblock having one or two distinct values, and new values 0..3 introduced in row major order

%C Column 4 of A209969

%H R. H. Hardin, <a href="/A209965/b209965.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 160*a(n-1) -9858*a(n-2) +286721*a(n-3) -3505459*a(n-4) -7704489*a(n-5) +640517305*a(n-6) -4759487502*a(n-7) -21219049490*a(n-8) +420859791361*a(n-9) -878171254221*a(n-10) -12643232573808*a(n-11) +66259330277918*a(n-12) +122870759491994*a(n-13) -1553376671736484*a(n-14) +1219539182999473*a(n-15) +17359779478680752*a(n-16) -39146051553201926*a(n-17) -91438263542603406*a(n-18) +373898684344261096*a(n-19) +116854653298320024*a(n-20) -1799083158352232088*a(n-21) +998160450833133144*a(n-22) +4801216485839890224*a(n-23) -5451035382131524304*a(n-24) -7054956173126826080*a(n-25) +12732134852398029184*a(n-26) +4672289972159061760*a(n-27) -16728156971141573696*a(n-28) +1059265242914046976*a(n-29) +13059429141341396224*a(n-30) -4207097515631301632*a(n-31) -5978493921676298752*a(n-32) +3137966625793618432*a(n-33) +1468906693869291520*a(n-34) -1139164366776567808*a(n-35) -134802883891748864*a(n-36) +213153759748931584*a(n-37) -11638547304415232*a(n-38) -18765649522720768*a(n-39) +2857764298162176*a(n-40) +564292134895616*a(n-41) -120413963157504*a(n-42) -2136276467712*a(n-43) +869730877440*a(n-44)

%e Some solutions for n=4

%e ..0..0..1..0..0....0..0..0..0..0....0..0..1..2..1....0..0..0..0..0

%e ..1..0..1..1..0....0..1..0..1..0....1..0..1..1..1....0..0..0..0..0

%e ..0..0..0..0..1....1..0..1..0..0....0..0..0..0..1....0..0..0..0..0

%e ..2..2..0..0..0....1..1..0..0..2....3..0..1..0..1....0..0..1..0..0

%e ..0..0..0..0..3....3..1..1..0..0....3..0..1..0..0....2..0..0..0..3

%K nonn

%O 1,1

%A _R. H. Hardin_ Mar 16 2012