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%I #5 Mar 31 2012 12:37:03
%S 40,61,61,102,46,102,188,31,31,188,342,28,22,28,342,590,38,27,27,38,
%T 590,1051,49,35,32,35,49,1051,1915,70,48,40,40,48,70,1915,3308,106,69,
%U 53,48,53,69,106,3308,5967,159,103,74,61,61,74,103,159,5967,10934,248,158,108
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..1 introduced in row major order
%C Table starts
%C ...40..61.102.188.342.590.1051.1915.3308.5967.10934.19151.34428.62824.110673
%C ...61..46..31..28..38..49...70..106..159..248...394...625..1002..1614...2599
%C ..102..31..22..27..35..48...69..103..158..247...391...624..1001..1611...2598
%C ..188..28..27..32..40..53...74..108..163..252...396...629..1006..1616...2603
%C ..342..38..35..40..48..61...82..116..171..260...404...637..1014..1624...2611
%C ..590..49..48..53..61..74...95..129..184..273...417...650..1027..1637...2624
%C .1051..70..69..74..82..95..116..150..205..294...438...671..1048..1658...2645
%C .1915.106.103.108.116.129..150..184..239..328...472...705..1082..1692...2679
%H R. H. Hardin, <a href="/A204754/b204754.txt">Table of n, a(n) for n = 1..1151</a>
%F Empirical for columns:
%F k>2: a(n) = 2*a(n-1) -a(n-3) for n>5
%F k=2: a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) for n>8
%F k=1: a(n) = 3*a(n-1) -2*a(n-2) +3*a(n-3) -10*a(n-4) +7*a(n-5) +7*a(n-6) -17*a(n-7) +6*a(n-8) +6*a(n-9) +4*a(n-10) -2*a(n-11) +4*a(n-12) -16*a(n-13) +8*a(n-14) for n>15
%e Some solutions for n=3 k=3
%e ..0..0..0..1..1....0..1..0..1..1....0..1..0..0..1....0..0..0..0..0
%e ..0..0..1..1..1....0..1..0..1..1....0..1..0..0..1....1..1..1..1..1
%e ..0..1..1..1..0....0..1..0..1..1....0..1..0..0..1....1..1..1..1..1
%e ..1..1..1..0..0....0..1..0..1..1....0..1..0..0..1....0..0..0..0..0
%e ..1..1..0..0..0....0..1..0..1..1....0..1..0..0..1....1..1..1..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 18 2012
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