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%I #4 Dec 19 2013 19:03:25
%S 32,80,80,192,152,192,512,296,296,512,1280,680,488,680,1280,3584,1544,
%T 968,968,1544,3584,9216,4040,1992,1640,1992,4040,9216,26624,9992,4808,
%U 2984,2984,4808,9992,26624,69632,28040,11336,6440,4904,6440,11336,28040
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9
%C Table starts
%C .....32.....80....192....512...1280...3584...9216..26624...69632..204800
%C .....80....152....296....680...1544...4040...9992..28040...72200..209672
%C ....192....296....488....968...1992...4808..11336..30536...76872..218696
%C ....512....680....968...1640...2984...6440..14120..35624...86312..236840
%C ...1280...1544...1992...2984...4904...9512..19368..45224..104360..271784
%C ...3584...4040...4808...6440...9512..16424..30632..65192..141224..342440
%C ...9216...9992..11336..14120..19368..30632..53288.104744..214056..481832
%C ..26624..28040..30536..35624..45224..65192.104744.189992..365864..766760
%C ..69632..72200..76872..86312.104360.141224.214056.365864..673832.1338920
%C .204800.209672.218696.236840.271784.342440.481832.766760.1338920.2532392
%H R. H. Hardin, <a href="/A234140/b234140.txt">Table of n, a(n) for n = 1..480</a>
%F Empirical for column k (the same recurrence apparently works on all rows and columns; the k=2 recurrence also works for k=1):
%F k=1: a(n) = 2*a(n-1) +8*a(n-2) -16*a(n-3)
%F k=2..7: a(n) = 3*a(n-1) +8*a(n-2) -30*a(n-3) +4*a(n-4) +48*a(n-5) -32*a(n-6)
%e Some solutions for n=5 k=4
%e ..3..0..0..0..3....0..3..0..3..0....3..2..2..0..3....0..3..2..3..0
%e ..0..0..3..0..0....0..0..0..0..0....2..0..3..2..2....0..0..2..0..0
%e ..3..0..0..0..3....3..0..3..0..3....3..2..2..0..3....0..3..2..3..0
%e ..0..0..3..0..0....2..2..2..2..2....2..0..3..2..2....0..0..2..0..0
%e ..0..3..3..3..0....3..0..3..0..3....3..2..2..0..3....0..3..2..3..0
%e ..0..0..3..0..0....1..1..1..1..1....2..0..3..2..2....2..2..0..2..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 19 2013