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T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum 3 and no antidiagonal sum 3 and no row sum 0 and no column sum 0
9

%I #4 Apr 09 2015 14:46:04

%S 153,393,393,857,570,857,2065,1564,1564,2065,5255,2512,2992,2512,5255,

%T 12914,6352,3752,3752,6352,12914,31032,12280,9112,5888,9112,12280,

%U 31032,75634,28816,16560,10360,10360,16560,28816,75634,185630,60728,38376

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum 3 and no antidiagonal sum 3 and no row sum 0 and no column sum 0

%C Table starts

%C ....153....393....857...2065...5255..12914...31032...75634..185630...453792

%C ....393....570...1564...2512...6352..12280...28816...60728..137768...311200

%C ....857...1564...2992...3752...9112..16560...38376...61376..135552...202832

%C ...2065...2512...3752...5888..10360..18688...33616...61568..112928...209024

%C ...5255...6352...9112..10360..22080..47440...96576..160704..300864...463632

%C ..12914..12280..16560..18688..47440..72192..155792..255488..600080...869632

%C ..31032..28816..38376..33616..96576.155792..404480..615296.1258112..1664400

%C ..75634..60728..61376..61568.160704.255488..615296..897280.2597504..3836160

%C .185630.137768.135552.112928.300864.600080.1258112.2597504.4353536..7208464

%C .453792.311200.202832.209024.463632.869632.1664400.3836160.7208464.14508288

%H R. H. Hardin, <a href="/A256748/b256748.txt">Table of n, a(n) for n = 1..2244</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 9] for n>12

%F k=2: [order 8] for n>13

%F k=3: [order 12] for n>17

%F k=4: [order 10] for n>14

%F k=5: [order 15] for n>18

%F k=6: [order 14] for n>18

%F k=7: [order 12] for n>15

%e Some solutions for n=4 k=4

%e ..0..1..0..1..1..0....1..1..0..0..1..1....0..1..0..1..0..0....1..1..0..0..1..1

%e ..1..1..0..0..1..1....0..1..1..1..1..0....0..1..0..1..0..1....0..0..1..1..1..0

%e ..0..1..1..1..0..0....1..1..0..0..1..1....1..1..1..1..1..1....1..1..0..0..1..1

%e ..1..1..0..0..1..1....0..0..1..1..0..0....1..0..1..0..1..0....0..1..1..1..0..0

%e ..0..1..1..1..0..0....1..1..0..0..1..1....0..0..1..0..1..0....1..1..0..0..1..1

%e ..0..1..0..0..1..0....0..1..1..1..0..0....0..1..0..1..1..1....0..1..1..1..1..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Apr 09 2015