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%I #4 Dec 19 2015 09:18:18
%S 1,3,3,2,8,2,7,50,50,7,19,1491,150,1491,19,35,7741,5582,5582,7741,35,
%T 77,82424,59454,1111758,59454,82424,77,176,763505,809199,74291246,
%U 74291246,809199,763505,176,377,6210500,12253344,4880049141,16816210911
%N T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal, vertical and antidiagonal neighbors less than or equal to itself.
%C Table starts
%C ...1.......3.........2..............7.................19..................35
%C ...3.......8........50...........1491...............7741...............82424
%C ...2......50.......150...........5582..............59454..............809199
%C ...7....1491......5582........1111758...........74291246..........4880049141
%C ..19....7741.....59454.......74291246........16816210911.......3057992438196
%C ..35...82424....809199.....4880049141......3057992438196....1826477943263851
%C ..77..763505..12253344...389508194942....853715037314662.1718918677426337400
%C .176.6210500.172499046.27699226366664.203178594217817141
%H R. H. Hardin, <a href="/A265965/b265965.txt">Table of n, a(n) for n = 1..83</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4)
%F k=2: [order 41]
%e Some solutions for n=3 k=4
%e ..0..4..1..2....2..2..3..1....0..3..3..1....1..4..0..2....0..2..1..0
%e ..2..1..6..0....0..6..0..4....2..6..0..4....0..2..6..1....3..6..5..3
%e ..3..2..1..2....2..2..4..0....2..1..4..0....3..3..1..2....1..0..2..0
%Y Column 1 is A196537.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Dec 19 2015