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%I #4 Dec 20 2015 07:44:05
%S 1,3,1,5,11,1,11,50,55,1,26,315,481,263,1,55,2142,5594,4659,1248,1,
%T 119,13796,121029,118489,45361,5959,1,263,89487,2045306,8260441,
%U 2482216,440405,28399,1,573,578659,33026298,408513208,576560236,52086421,4281953
%N T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal and antidiagonal neighbors less than itself.
%C Table starts
%C .1.......3..........5.............11.................26......................55
%C .1......11.........50............315...............2142...................13796
%C .1......55........481...........5594.............121029.................2045306
%C .1.....263.......4659.........118489............8260441...............408513208
%C .1....1248......45361........2482216..........576560236.............82171346791
%C .1....5959.....440405.......52086421........40462691139..........16683384355551
%C .1...28399....4281953.....1092258910......2834665076351........3378465528248312
%C .1..135383...41605113....22909266015....198722506983924......684927787385220826
%C .1..645407..404371841...480473869537..13929598180007373...138808963888717658013
%C .1.3076736.3929676961.10077157027608.976418236686388550.28134602812633017755802
%H R. H. Hardin, <a href="/A266033/b266033.txt">Table of n, a(n) for n = 1..143</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 3*a(n-1) +7*a(n-2) +7*a(n-3) -a(n-4)
%F k=3: a(n) = 5*a(n-1) +46*a(n-2) +6*a(n-3) -72*a(n-4)
%F k=4: [order 16] for n>17
%F k=5: [order 38] for n>41
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4)
%F n=2: [order 26]
%e Some solutions for n=4 k=4
%e ..0..0..3..1....0..0..1..1....0..0..3..1....0..2..3..0....0..1..1..2
%e ..1..1..0..1....2..1..0..0....2..0..0..0....1..0..0..2....2..0..0..0
%e ..1..0..1..1....2..0..0..1....2..0..4..1....1..4..0..1....2..1..4..1
%e ..0..3..0..0....1..1..3..0....1..2..0..1....0..0..3..0....2..0..0..0
%Y Row 1 is A196423.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Dec 20 2015
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