A302322 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 20, 25, 8, 16, 52, 65, 81, 16, 32, 136, 177, 281, 264, 32, 64, 360, 519, 953, 1144, 857, 64, 128, 960, 1528, 3559, 4525, 4321, 2785, 128, 256, 2576, 4509, 14022, 20686, 19734, 18093, 9050, 256, 512, 6944, 13329, 55727, 104932, 110035

Offset

1,2

Comments

Table starts

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

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

...4....25.....65.....177......519......1528.......4509.......13329

...8....81....281.....953.....3559.....14022......55727......218945

..16...264...1144....4525....20686....104932.....529381.....2593409

..32...857...4321...19734...110035....708572....4521584....27478634

..64..2785..18093...96956...659949...5542827...45861206...349722102

.128..9050..72746..458537..3834162..41843808..444688101..4252740185

.256.29407.285199.2098489.21619209.305929316.4176914829.49936266116

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 14]

k=4: [order 48] for n>49

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 14] for n>15

n=4: [order 57] for n>58

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240478.

Row 1 is A000079(n-1).

Sequence in context: A302623 A302415 A303182 * A303016 A302820 A303513

Adjacent sequences: A302319 A302320 A302321 * A302323 A302324 A302325

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 05 2018

Status

approved