A253698 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock ne-sw antidiagonal difference unequal to its neighbors horizontally and nw+se diagonal sum unequal to its neighbors vertically

16, 40, 40, 104, 76, 104, 264, 150, 146, 264, 680, 282, 234, 304, 680, 1736, 540, 356, 480, 602, 1736, 4456, 1026, 618, 700, 878, 1182, 4456, 11400, 1984, 968, 992, 1120, 1472, 2416, 11400, 29224, 3782, 1608, 1262, 1632, 1638, 2982, 4772, 29224, 74824

Offset

1,1

Comments

Table starts

....16....40...104...264...680..1736..4456.11400.29224.74824.191720.491016

....40....76...150...282...540..1026..1984..3782..7270.13880..26644..51026

...104...146...234...356...618...968..1608..2558..4278..6854..11266..18192

...264...304...480...700...992..1262..1790..2538..4020..5990...8836..12394

...680...602...878..1120..1632..1914..2626..3598..5568..7834..11444..15184

..1736..1182..1472..1638..2386..3042..4010..5178..6934..8938..12212..16174

..4456..2416..2982..3136..4180..5030..6558..8846.12620.17170..22264..27490

.11400..4772..5282..4782..6552..7800.10428.14710.20260.27658..35292..45002

.29224..9652..9880..7926.10696.12646.16796.22964.30864.42644..55562..75580

.74824.19152.18552.14462.18236.20932.26124.36540.51630.74332..93964.121868

Links

R. H. Hardin, Table of n, a(n) for n = 1..1289

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +4*a(n-2)

k=2: [order 16]

k=3: [order 19] for n>21

k=4: [order 22] for n>24

k=5: [order 26] for n>31

k=6: [order 28] for n>33

k=7: [order 32] for n>38

Empirical for row n:

n=1: a(n) = a(n-1) +4*a(n-2)

n=2: [order 16]

n=3: [order 19] for n>21

n=4: [order 19] for n>26

n=5: [order 27] for n>34

n=6: [order 21] for n>31

n=7: [order 25] for n>37

Example

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

Crossrefs

Column 1 and row 1 are A185761

Sequence in context: A070584 A205072 A185798 * A185769 A205255 A176869

Adjacent sequences: A253695 A253696 A253697 * A253699 A253700 A253701

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 09 2015

Status

approved