A302150 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 1, 4, 1, 2, 1, 8, 1, 2, 4, 1, 16, 1, 3, 5, 10, 1, 32, 1, 6, 11, 17, 28, 1, 64, 1, 10, 34, 56, 65, 84, 1, 128, 1, 21, 88, 255, 289, 257, 260, 1, 256, 1, 42, 271, 1038, 2005, 1529, 1025, 816, 1, 512, 1, 86, 798, 4771, 12212, 15999, 8152, 4097, 2576, 1, 1024, 1, 179

Offset: 1

Author

R. H. Hardin, Apr 02 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1.1....1.....1......1.......1.........1..........1............1

...2.1....2.....2......3.......6........10.........21...........42

...4.1....4.....5.....11......34........88........271..........798

...8.1...10....17.....56.....255......1038.......4771........21866

..16.1...28....65....289....2005.....12212......83092.......578398

..32.1...84...257...1529...15999....145150....1482725.....15902462

..64.1..260..1025...8152..128319...1728734...26544210....439103633

.128.1..816..4097..43676.1030709..20614702..476725579..12181287002

.256.1.2576.16385.234707.8283143.245896061.8575073202.338788296901

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..363

Crossrefs

Column 1 is A000079(n-1).

Column 4 is A052539(n-2).

Row 2 is A240513(n-3).

Formula

Empirical for column k:

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

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

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

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

k=5: [order 12]

k=6: [order 7] for n>9

k=7: [order 51] for n>54

Empirical for row n:

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

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

n=3: [order 25] for n>27

n=4: [order 85] for n>89