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A234122 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

%I A234122 #6 Jun 02 2025 09:12:23
%S A234122 31,145,145,673,1361,673,3127,12593,12593,3127,14527,116801,231713,
%T A234122 116801,14527,67489,1082977,4279065,4279065,1082977,67489,313537,
%U A234122 10041953,79003521,157630963,79003521,10041953,313537,1456615,93113761
%N A234122 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.
%C A234122 Table starts
%C A234122 .......31.........145.............673...............3127.................14527
%C A234122 ......145........1361...........12593.............116801...............1082977
%C A234122 ......673.......12593..........231713............4279065..............79003521
%C A234122 .....3127......116801.........4279065..........157630963............5807422543
%C A234122 ....14527.....1082977........79003521.........5807422543..........427196005695
%C A234122 ....67489....10041953......1458813409.......214027901025........31446640848897
%C A234122 ...313537....93113761.....26937444801......7888454356625......2315408571668225
%C A234122 ..1456615...863396401....497411686793....290756314787875....170502665692732079
%C A234122 ..6767071..8005833073...9184935953377..10716964158533127..12556134956123911615
%C A234122 .31438129.74233997105.169604155276817.395017615132720993.924677153131389366689
%H A234122 R. H. Hardin, <a href="/A234122/b234122.txt">Table of n, a(n) for n = 1..364</a>
%F A234122 Empirical for column k:
%F A234122 k=1: a(n) = 4*a(n-1) +3*a(n-2)
%F A234122 k=2: a(n) = 10*a(n-1) -4*a(n-2) -26*a(n-3) +5*a(n-4)
%F A234122 k=3: a(n) = 20*a(n-1) -10*a(n-2) -324*a(n-3) -277*a(n-4) +144*a(n-5)
%F A234122 k=4: [order 11]
%F A234122 k=5: [order 17]
%F A234122 k=6: [order 35]
%F A234122 k=7: [order 62]
%e A234122 Some solutions for n=2 k=4
%e A234122 ..0..1..0..0..1....0..1..2..2..2....1..2..1..2..2....0..1..0..1..2
%e A234122 ..1..0..1..0..1....1..1..1..1..2....1..2..2..2..2....1..0..0..1..2
%e A234122 ..1..1..0..0..1....1..2..2..1..2....2..1..1..1..2....0..1..0..1..1
%Y A234122 Column 1 is A086901(n+3)
%K A234122 nonn,tabl
%O A234122 1,1
%A A234122 _R. H. Hardin_, Dec 19 2013