A302069 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 25, 32, 8, 16, 81, 148, 128, 16, 32, 263, 748, 884, 512, 32, 64, 855, 3657, 7070, 5296, 2048, 64, 128, 2778, 18108, 54177, 67070, 31760, 8192, 128, 256, 9027, 89658, 420121, 807601, 636852, 190528, 32768, 256, 512, 29333, 444359

Offset

1,2

Comments

Table starts

...1......2.......4.........8..........16............32..............64

...2......8......25........81.........263...........855............2778

...4.....32.....148.......748........3657.........18108...........89658

...8....128.....884......7070.......54177........420121.........3247765

..16....512....5296.....67070......807601.......9825815.......119508742

..32...2048...31760....636852....12063625.....230634314......4418931065

..64...8192..190528...6048836...180330117....5420105343....163660519064

.128..32768.1143104..57457232..2696254757..127431664603...6065045335103

.256.131072.6858496.545796112.40316943551.2996509042607.224815724811979

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

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

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

k=3: a(n) = 8*a(n-1) -12*a(n-2) for n>3

k=4: a(n) = 16*a(n-1) -76*a(n-2) +148*a(n-3) -124*a(n-4) +36*a(n-5) for n>6

k=5: [order 11] for n>13

k=6: [order 25] for n>27

k=7: [order 53] for n>56

Empirical for row n:

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

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

n=3: [order 15] for n>18

n=4: [order 53] for n>58

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Row 1 is A000079(n-1).

Row 2 is A301842.

Sequence in context: A299180 A299942 A301841 * A298195 A299089 A299345

Adjacent sequences: A302066 A302067 A302068 * A302070 A302071 A302072

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 31 2018

Status

approved