A230708 T(n,k)=Number of (n+3)X(k+3) 0..2 white 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, 28, 30, 102, 244, 244, 102, 348, 800, 2106, 800, 348, 1172, 6576, 16536, 16536, 6576, 1172, 3956, 21076, 130446, 121382, 130446, 21076, 3956, 13326, 173428, 1025430, 2382398, 2382398, 1025430, 173428, 13326, 44916, 554040, 8053490

Offset: 1

Author

R. H. Hardin, Oct 28 2013

Keywords

• nonn
• tabl

Comments

Table starts

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

.....8.....28......244........800.........6576..........21076...........173428

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

...102....800....16536.....121382......2382398.......17497342........342031378

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

..1172..21076..1025430...17497342....801845362....13663471254.....625553036008

..3956.173428..8053490..342031378..14669811856...625553036008...26681634560690

.13326.554040.63237238.2508344646.268320990890.10652997961328.1137681116923966

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..219

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]