A280673 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 2, 4, 11, 5, 11, 59, 82, 14, 30, 338, 858, 612, 41, 82, 1917, 10205, 12484, 4568, 122, 224, 10893, 119440, 310365, 181640, 34096, 365, 612, 61880, 1401470, 7533245, 9439606, 2642832, 254496, 1094, 1672, 351541, 16438612, 183331502, 474736149

Offset

1,2

Comments

Table starts

....1.........2............4..............11...............30................82

....2........11...........59.............338.............1917.............10893

....5........82..........858...........10205...........119440...........1401470

...14.......612........12484..........310365..........7533245.........183331502

...41......4568.......181640.........9439606........474736149.......23952262535

..122.....34096......2642832.......287101721......29920114246.....3130289979912

..365....254496.....38452768......8732086113....1885698283255...409089889172506

.1094...1899584....559481408....265582964074..118845116023725.53463025958093933

.3281..14178688...8140361856...8077601392565.7490149091439288

.9842.105831168.118440917248.245677069239189

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -3*a(n-2)

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

k=3: a(n) = 14*a(n-1) +8*a(n-2)

k=4: a(n) = 29*a(n-1) +44*a(n-2) -27*a(n-3) -81*a(n-4) for n>5

k=5: [order 8] for n>9

k=6: [order 20] for n>22

Empirical for row n:

n=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4

n=2: a(n) = 5*a(n-1) +6*a(n-2) -11*a(n-3) -7*a(n-4) +4*a(n-5) for n>6

n=3: [order 18] for n>20

n=4: [order 73] for n>78

Example

Some solutions for n=3 k=4
..0..1..0..0. .0..1..0..2. .0..1..0..1. .0..0..1..0. .0..1..1..0
..0..1..2..1. .2..0..2..1. .0..2..1..0. .2..2..1..1. .2..0..2..0
..1..2..0..0. .2..1..0..2. .2..0..2..0. .1..0..2..2. .1..0..1..1

Crossrefs

Column 1 is A007051(n-1).

Column 2 is A209094.

Row 1 is A021006(n-3).

Sequence in context: A219985 A220800 A220786 * A363385 A280531 A072074

Adjacent sequences: A280670 A280671 A280672 * A280674 A280675 A280676

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 07 2017

Status

approved