A303182 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 17, 25, 8, 16, 37, 31, 81, 16, 32, 78, 72, 135, 264, 32, 64, 169, 170, 297, 547, 857, 64, 128, 361, 382, 931, 1302, 1938, 2785, 128, 256, 778, 873, 2569, 5613, 5050, 6965, 9050, 256, 512, 1673, 2013, 6668, 24751, 29124, 20188, 25953, 29407, 512

Offset

1,2

Comments

Table starts

...1.....2.....4......8......16........32.........64.........128..........256

...2.....8....17.....37......78.......169........361.........778.........1673

...4....25....31.....72.....170.......382........873........2013.........4618

...8....81...135....297.....931......2569.......6668.......17934........48674

..16...264...547...1302....5613.....24751......88153......325770......1253442

..32...857..1938...5050...29124....218980....1064399.....5463686.....31140302

..64..2785..6965..20188..148501...1803435...11901719....82524101....673749714

.128..9050.25953..81926..786247..15559135..141429948..1341217380..15951682785

.256.29407.95602.329957.4126586.133939941.1665576584.21624053966.375045359077

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

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 13]

k=4: [order 31] for n>33

k=5: [order 66] for n>73

Empirical for row n:

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

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

n=3: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -3*a(n-4) +a(n-5) for n>9

n=4: [order 17] for n>22

n=5: [order 34] for n>40

n=6: [order 84] for n>90

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240478.

Row 1 is A000079(n-1).

Row 2 is A281470.

Sequence in context: A281469 A302623 A302415 * A302322 A303016 A302820

Adjacent sequences: A303179 A303180 A303181 * A303183 A303184 A303185

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 19 2018

Status

approved