A258921 - OEIS

%I #4 Jun 14 2015 21:39:55

%S 200,576,576,1680,1156,1680,5184,1936,1936,5184,15840,4096,1200,4096,

%T 15840,46656,9216,1024,1024,9216,46656,138240,17424,1440,576,1440,

%U 17424,138240,419904,30976,1600,576,576,1600,30976,419904,1270080,66564,1568

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

%C Table starts

%C .....200....576.1680.5184.15840.46656.138240.419904.1270080.3779136.11275200

%C .....576...1156.1936.4096..9216.17424..30976..66564..141376..264196...501264

%C ....1680...1936.1200.1024..1440..1600...1568...1936....2560....2704.....2592

%C ....5184...4096.1024..576...576...784....576....576.....576.....784......576

%C ...15840...9216.1440..576...512...576....640....576.....512.....576......640

%C ...46656..17424.1600..784...576...576....576....784.....576.....576......576

%C ..138240..30976.1568..576...640...576....512....576.....640.....576......512

%C ..419904..66564.1936..576...576...784....576....576.....576.....784......576

%C .1270080.141376.2560..576...512...576....640....576.....512.....576......640

%C .3779136.264196.2704..784...576...576....576....784.....576.....576......576

%H R. H. Hardin, <a href="/A258921/b258921.txt">Table of n, a(n) for n = 1..6374</a>

%F Empirical for diagonal and column k:

%F diagonal: a(n) = a(n-2) for n>5

%F k=1: a(n) = 3*a(n-1) -6*a(n-2) +18*a(n-3)

%F k=2: [order 28]

%F k=3: [order 10] for n>13

%F k=4: a(n) = a(n-4) for n>7

%F k=5: a(n) = a(n-1) -a(n-2) +a(n-3) for n>6

%F k=6: a(n) = a(n-4) for n>7

%F k=7: a(n) = a(n-1) -a(n-2) +a(n-3) for n>6

%F Empirical periodic behavior for diagonal and column k:

%F diagonal: apparent period of length 2 starting at n=4: 576 512

%F k=4: apparent period of length 4 starting at n=4: 576 576 784 576

%F k=5: apparent period of length 4 starting at n=4: 576 512 576 640

%F k=6: apparent period of length 4 starting at n=4: 784 576 576 576

%F k=7: apparent period of length 4 starting at n=4: 576 640 576 512

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jun 14 2015