

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 2x(i,j)


5



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
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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



FORMULA

Empirical for column k:
k=1: a(n) = a(n1) for n>1
k=2: a(n) = a(n1) +2*a(n2)
k=3: a(n) = 9*a(n2) 4*a(n4)
k=4: a(n) = 3*a(n1) +8*a(n2) a(n3) a(n4) for n>5
k=5: a(n) = 59*a(n2) 230*a(n4) 2*a(n6) +32*a(n8) 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



KEYWORD



AUTHOR



STATUS

approved



