A302889 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 37, 3, 16, 1, 72, 53, 141, 6, 32, 1, 168, 197, 238, 569, 10, 64, 1, 496, 818, 2278, 1102, 2262, 21, 128, 1, 1296, 2548, 12782, 20937, 5570, 8968, 42, 256, 1, 3616, 10926, 98458, 200186, 206332, 28594, 35667, 86, 512, 1, 9760, 42671

Offset: 1

Author

R. H. Hardin, Apr 15 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1..1......1......1.........1...........1.............1...............1

...2..2.....12.....20........72.........168...........496............1296

...4..2.....37.....53.......197.........818..........2548...........10926

...8..3....141....238......2278.......12782.........98458..........714934

..16..6....569...1102.....20937......200186.......2727690........37626360

..32.10...2262...5570....206332.....3452246......89290791......2247650354

..64.21...8968..28594...2059835....60501563....2899297652....133518102376

.128.42..35667.149206..20622709..1073161270...94799190457...7977498513759

.256.86.141839.788373.206851726.19073141368.3098646840396.476377988322833

Examples

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

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A302368.

Formula

Empirical for column k:

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

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

k=3: [order 10]

k=4: [order 35] for n>37

Empirical for row n:

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

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

n=3: [order 16] for n>17

n=4: [order 51] for n>54