A230739 T(n,k)=Number of (n+3)X(k+3) 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero

2, 8, 8, 30, 66, 30, 102, 244, 244, 102, 348, 2016, 2106, 2016, 348, 1172, 6576, 16536, 16536, 6576, 1172, 3956, 54138, 130446, 320970, 130446, 54138, 3956, 13326, 173428, 1025430, 2382398, 2382398, 1025430, 173428, 13326, 44916, 1427040, 8053490

Offset

1,1

Comments

Table starts

.....2.......8.......30........102..........348...........1172.............3956

.....8......66......244.......2016.........6576..........54138...........173428

....30.....244.....2106......16536.......130446........1025430..........8053490

...102....2016....16536.....320970......2382398.......46599682........342031378

...348....6576...130446....2382398.....43853402......801845362......14669811856

..1172...54138..1025430...46599682....801845362....36695929036.....625553036008

..3956..173428..8053490..342031378..14669811856...625553036008...26681634560690

.13326.1427040.63237238.6692078688.268320990890.28644012159382.1137681116923966

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: a(n) = 31*a(n-2) -126*a(n-4) +42*a(n-6) +79*a(n-8) -a(n-10) +8*a(n-12)

k=3: [order 22]

k=4: [order 50]

Example

Some solutions for n=3 k=4
..x..0..x..0..x..2..x....x..0..x..2..x..2..x....x..0..x..0..x..1..x
..1..x..1..x..1..x..0....2..x..1..x..0..x..1....1..x..1..x..2..x..0
..x..2..x..0..x..1..x....x..0..x..1..x..1..x....x..2..x..0..x..2..x
..1..x..0..x..2..x..0....1..x..0..x..2..x..0....1..x..0..x..2..x..0
..x..2..x..1..x..1..x....x..2..x..0..x..2..x....x..2..x..1..x..1..x
..1..x..1..x..0..x..0....1..x..2..x..1..x..1....1..x..0..x..0..x..0

Crossrefs

Column 1 is A230701

Column 3 is A230703

Column 5 is A230705

Column 7 is A230707

Sequence in context: A250313 A180825 A230708 * A227326 A323852 A064231

Adjacent sequences: A230736 A230737 A230738 * A230740 A230741 A230742

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 28 2013

Status

approved