A258921 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

200, 576, 576, 1680, 1156, 1680, 5184, 1936, 1936, 5184, 15840, 4096, 1200, 4096, 15840, 46656, 9216, 1024, 1024, 9216, 46656, 138240, 17424, 1440, 576, 1440, 17424, 138240, 419904, 30976, 1600, 576, 576, 1600, 30976, 419904, 1270080, 66564, 1568

Offset

1,1

Comments

Table starts

.....200....576.1680.5184.15840.46656.138240.419904.1270080.3779136.11275200

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

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

....5184...4096.1024..576...576...784....576....576.....576.....784......576

...15840...9216.1440..576...512...576....640....576.....512.....576......640

...46656..17424.1600..784...576...576....576....784.....576.....576......576

..138240..30976.1568..576...640...576....512....576.....640.....576......512

..419904..66564.1936..576...576...784....576....576.....576.....784......576

.1270080.141376.2560..576...512...576....640....576.....512.....576......640

.3779136.264196.2704..784...576...576....576....784.....576.....576......576

Links

R. H. Hardin, Table of n, a(n) for n = 1..6374

Formula

Empirical for diagonal and column k:

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

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

k=2: [order 28]

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

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

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

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

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

Empirical periodic behavior for diagonal and column k:

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

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

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

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

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

Example

Some solutions for n=4 k=4
..1..1..0..1..1..0....1..1..0..1..0..0....1..1..1..1..0..0....1..0..1..0..0..1
..1..1..0..1..0..0....1..1..0..0..0..0....0..1..0..1..1..0....0..0..0..1..1..1
..0..1..1..0..1..0....0..1..0..0..1..0....1..0..0..1..0..1....0..1..1..0..1..0
..0..1..0..0..1..0....0..0..0..0..1..1....1..1..0..0..0..0....1..0..0..0..0..1
..1..0..1..0..0..1....0..0..1..0..1..1....0..0..0..0..1..1....0..1..0..1..1..0
..0..0..1..0..1..1....0..0..1..1..1..1....0..0..1..0..0..1....1..1..1..0..0..0

Crossrefs

Sequence in context: A004966 A117412 A109632 * A258918 A129641 A202966

Adjacent sequences: A258918 A258919 A258920 * A258922 A258923 A258924

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 14 2015

Status

approved