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Number of (n+1)X(6+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1
1

%I #4 Dec 19 2013 17:45:26

%S 67489,10041953,1458813409,214027901025,31446640848897,

%T 4625943683805313,680845368964238145,100232847106041668353,

%U 14757962542814417545441,2173049645779146516000801,319982366490305655551327777

%N Number of (n+1)X(6+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1

%C Column 6 of A234122

%H R. H. Hardin, <a href="/A234120/b234120.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 261*a(n-1) -18560*a(n-2) +127208*a(n-3) +23755242*a(n-4) -406238978*a(n-5) -11768024848*a(n-6) +211536189168*a(n-7) +3167620020453*a(n-8) -43174324632265*a(n-9) -498144039526280*a(n-10) +3974314857666608*a(n-11) +43883259123774428*a(n-12) -167685268616512940*a(n-13) -2040900846762609856*a(n-14) +3445445946343381888*a(n-15) +52296679884037531065*a(n-16) -35833370093864352573*a(n-17) -776126649677016939696*a(n-18) +226412171176325558120*a(n-19) +6916149301019844647706*a(n-20) -1682665179571062843826*a(n-21) -37312103086122262303664*a(n-22) +14659167338730178934224*a(n-23) +117646777156101371452739*a(n-24) -76253461020753171154783*a(n-25) -192817994631326898576392*a(n-26) +189380280584489465020224*a(n-27) +110172317785328612275008*a(n-28) -187529085888044105270592*a(n-29) +38102718853877138892864*a(n-30) +32573701148082394908672*a(n-31) -13221821267594299551744*a(n-32) -630264421714516770816*a(n-33) +672250225845986131968*a(n-34) -28475524214125756416*a(n-35)

%e Some solutions for n=1

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2013