A303016 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 20, 25, 8, 16, 52, 68, 81, 16, 32, 136, 187, 308, 264, 32, 64, 360, 579, 1047, 1320, 857, 64, 128, 960, 1797, 4237, 5299, 5220, 2785, 128, 256, 2576, 5571, 18513, 27719, 24030, 22652, 9050, 256, 512, 6944, 17382, 79945, 166978, 160253

Offset

1,2

Comments

Table starts

...1.....2......4.......8.......16........32..........64..........128

...2.....8.....20......52......136.......360.........960.........2576

...4....25.....68.....187......579......1797........5571........17382

...8....81....308....1047.....4237.....18513.......79945.......344190

..16...264...1320....5299....27719....166978......970892......5570473

..32...857...5220...24030...160253...1298140.....9976891.....75234550

..64..2785..22652..123538..1044810..11644063...121524556...1219773362

.128..9050..95220..612923..6647878.101648313..1423906011..18974341664

.256.29407.390580.2935811.40950485.858924912.16163776349.285987277414

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 10]

k=4: [order 43] for n>44

Empirical for row n:

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

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

n=3: [order 15] for n>16

n=4: [order 62] for n>64

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240478.

Row 1 is A000079(n-1).

Row 2 is A302323.

Sequence in context: A302415 A303182 A302322 * A302820 A303513 A303727

Adjacent sequences: A303013 A303014 A303015 * A303017 A303018 A303019

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 17 2018

Status

approved