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

Author

R. H. Hardin, Oct 28 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A230701

Column 3 is A230703

Column 5 is A230705

Column 7 is A230707

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]