A230661 T(n,k)=Number of nXk 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j)

1, 0, 0, 0, 3, 0, 0, 3, 3, 0, 0, 9, 15, 9, 0, 0, 15, 21, 21, 15, 0, 0, 33, 135, 123, 135, 33, 0, 0, 63, 177, 531, 531, 177, 63, 0, 0, 129, 1155, 2547, 8613, 2547, 1155, 129, 0, 0, 255, 1509, 11745, 28161, 28161, 11745, 1509, 255, 0, 0, 513, 9855, 54957, 477279, 337977

Offset

1,5

Comments

Table starts

.1...0....0.....0.......0........0..........0...........0.............0

.0...3....3.....9......15.......33.........63.........129...........255

.0...3...15....21.....135......177.......1155........1509..........9855

.0...9...21...123.....531.....2547......11745.......54957........255753

.0..15..135...531....8613....28161.....477279.....1539207......26178201

.0..33..177..2547...28161...337977....3951657....46564959.....547445439

.0..63.1155.11745..477279..3951657..169006665..1374288243...59075291211

.0.129.1509.54957.1539207.46564959.1374288243.40860127671.1212230763441

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

k=1: a(n) = a(n-1) for n>1

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

k=3: a(n) = 9*a(n-2) -4*a(n-4)

k=4: a(n) = 3*a(n-1) +8*a(n-2) -a(n-3) -a(n-4) for n>5

k=5: a(n) = 59*a(n-2) -230*a(n-4) -2*a(n-6) +32*a(n-8) for n>10

k=6: [order 23] for n>24

k=7: [order 46] for n>47

Example

Some solutions for n=5 k=4
..x..0..x..1....x..1..x..0....x..2..x..2....x..2..x..1....x..2..x..2
..2..x..1..x....1..x..2..x....2..x..0..x....0..x..1..x....0..x..0..x
..x..2..x..1....x..0..x..0....x..0..x..0....x..0..x..2....x..1..x..0
..0..x..0..x....2..x..0..x....0..x..2..x....2..x..0..x....1..x..2..x
..x..2..x..2....x..0..x..2....x..2..x..0....x..0..x..2....x..1..x..0

Crossrefs

Column 2 is A062510(n-1)

Column 4 is A230648

Column 6 is A230650

Sequence in context: A075874 A181634 A230652 * A178952 A178153 A267794

Adjacent sequences: A230658 A230659 A230660 * A230662 A230663 A230664

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 27 2013

Status

approved