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%I #4 Dec 21 2015 08:20:40
%S 1,3,1,4,5,1,5,13,16,1,9,36,64,39,1,16,100,161,230,105,1,25,233,736,
%T 929,1012,272,1,39,680,3846,6307,4893,3928,715,1,64,2201,16103,52171,
%U 53442,26948,16428,1869,1,105,6508,62778,371130,841668,457738,145274,65736
%N T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal and antidiagonal neighbors exactly one smaller than itself.
%C Table starts
%C .1.....3.......4........5..........9...........16.............25
%C .1.....5......13.......36........100..........233............680
%C .1....16......64......161........736.........3846..........16103
%C .1....39.....230......929.......6307........52171.........371130
%C .1...105....1012.....4893......53442.......841668........9880139
%C .1...272....3928....26948.....457738.....12401485......240721036
%C .1...715...16428...145274....3899732....192212829.....6206090116
%C .1..1869...65736...790986...33335734...2895851074...154469020054
%C .1..4896..269908..4286644..284461696..44366390231..3932140956510
%C .1.12815.1091720.23281595.2429715557.672954998752.98694163378141
%H R. H. Hardin, <a href="/A266101/b266101.txt">Table of n, a(n) for n = 1..161</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
%F k=3: a(n) = a(n-1) +12*a(n-2) +5*a(n-3) -12*a(n-4) -2*a(n-5)
%F k=4: [order 15] for n>16
%F k=5: [order 17] for n>20
%F k=6: [order 72] for n>75
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-3) +a(n-4)
%F n=2: [order 16] for n>19
%F n=3: [order 64] for n>68
%e Some solutions for n=4 k=4
%e ..1..0..1..1....0..1..2..1....0..1..2..1....0..0..0..1....1..0..0..0
%e ..0..2..0..1....1..0..0..1....1..0..0..1....1..1..1..0....1..2..1..2
%e ..1..0..1..2....1..2..1..1....1..1..1..1....2..1..1..2....0..1..1..1
%e ..0..1..1..0....0..0..0..1....1..0..0..0....0..2..1..0....1..0..0..1
%Y Column 2 is A121646(n+2).
%Y Row 1 is A195971.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Dec 21 2015
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