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A253367 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 2X2 and 3X3 subblock diagonal maximum minus antidiagonal minimum unequal to its neighbors horizontally and vertically 9

%I #4 Dec 30 2014 17:26:01

%S 152,272,272,560,424,560,976,960,960,976,1904,1536,2992,1536,1904,

%T 3472,3136,5280,5280,3136,3472,6544,5664,13800,8904,13800,5664,6544,

%U 12048,10496,27072,23936,23936,27072,10496,12048,22704,20000,63496,53128,76840

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 2X2 and 3X3 subblock diagonal maximum minus antidiagonal minimum unequal to its neighbors horizontally and vertically

%C Table starts

%C ...152...272....560.....976....1904.....3472......6544.....12048......22704

%C ...272...424....960....1536....3136.....5664.....10496.....20000......36160

%C ...560...960...2992....5280...13800....27072.....63496....130464.....297288

%C ...976..1536...5280....8904...23936....53128....112864....286888.....563680

%C ..1904..3136..13800...23936...76840...175328....438504...1151296....2656232

%C ..3472..5664..27072...53128..175328...520888...1255456...4289736....9455136

%C ..6544.10496..63496..112864..438504..1255456...3424264..12086016...30463848

%C .12048.20000.130464..286888.1151296..4289736..12086016..51091912..132958016

%C .22704.36160.297288..563680.2656232..9455136..30463848.132958016..419412744

%C .41680.68672.612480.1423176.7032608.31254904.105411360.528171592.1709806624

%H R. H. Hardin, <a href="/A253367/b253367.txt">Table of n, a(n) for n = 1..1057</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-2) -3*a(n-4) +4*a(n-6)

%F k=2: a(n) = 5*a(n-2) -8*a(n-4) +8*a(n-6) +4*a(n-8)

%F k=3: a(n) = 7*a(n-2) -15*a(n-4) +17*a(n-6) +16*a(n-8) for n>11

%F k=4: [order 14] for n>16

%F k=5: [order 16] for n>19

%F k=6: [order 22] for n>26

%F k=7: [order 30] for n>33

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 30 2014

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Last modified February 23 09:02 EST 2024. Contains 370276 sequences. (Running on oeis4.)