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%I #4 Dec 20 2015 11:22:55
%S 1,3,3,4,17,4,5,35,35,5,9,89,34,89,9,16,323,81,81,323,16,25,1057,809,
%T 525,809,1057,25,39,3027,1750,8262,8262,1750,3027,39,64,9257,5071,
%U 25663,154939,25663,5071,9257,64,105,29835,29256,148323,1066148,1066148,148323
%N T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal, vertical, diagonal and antidiagonal neighbors exactly one smaller than itself.
%C Table starts
%C ...1.....3......4.......5.........9........16........25.........39.........64
%C ...3....17.....35......89.......323......1057......3027.......9257......29835
%C ...4....35.....34......81.......809......1750......5071......29256......93170
%C ...5....89.....81.....525......8262.....25663....148323....1480037....7361668
%C ...9...323....809....8262....154939...1066148..11753249..164649556.1624261580
%C ..16..1057...1750...25663...1066148..11211992.156829155.3678276863
%C ..25..3027...5071..148323..11753249.156829155
%C ..39..9257..29256.1480037.164649556
%C ..64.29835..93170.7361668
%C .105.92561.300067
%H R. H. Hardin, <a href="/A266067/b266067.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-3) +a(n-4)
%F k=2: [order 18]
%F k=3: [order 78]
%e Some solutions for n=4 k=4
%e ..0..0..0..1....2..1..0..0....1..0..0..1....1..0..0..0....1..1..2..0
%e ..0..2..3..2....1..3..2..0....2..2..2..2....1..2..3..0....0..2..2..1
%e ..1..1..2..1....2..0..3..1....1..3..3..1....2..2..2..0....0..3..2..2
%e ..2..3..2..0....1..2..1..2....0..1..1..0....0..1..2..1....0..0..0..1
%Y Column 1 is A195971.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Dec 20 2015