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

1,1

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

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]

Example

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

Crossrefs

Sequence in context: A146749 A250313 A180825 * A230739 A227326 A323852

Adjacent sequences: A230705 A230706 A230707 * A230709 A230710 A230711

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 28 2013

Status

approved