A302680 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 4, 5, 3, 4, 8, 8, 5, 8, 6, 16, 13, 7, 12, 7, 9, 32, 21, 13, 18, 20, 11, 14, 64, 34, 23, 40, 30, 33, 18, 22, 128, 55, 37, 94, 76, 63, 64, 29, 35, 256, 89, 63, 184, 217, 187, 125, 121, 47, 56, 512, 144, 109, 358, 509, 661, 453, 257, 231, 76, 90, 1024, 233, 183, 760

Offset: 1

Author

R. H. Hardin, Apr 11 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1..2..3...5....8...13....21.....34......55.......89......144.......233

...2..3..3...5....7...13....23.....37......63......109......183.......309

...4..4..8..12...18...40....94....184.....358......760.....1594......3220

...8..6..7..20...30...76...217....509....1189.....3034.....7569.....18274

..16..9.11..33...63..187...661...1837....5075....15661....46975....135191

..32.14.18..64..125..453..2013...6725...21745....80985...295335...1015113

..64.22.29.121..257.1125..6311..25139...96728...439233..1942666...8017639

.128.35.47.231..528.2782.19497..92889..422915..2330640.12480973..61679118

.256.56.76.440.1085.6843.60253.343421.1847358.12346637.80210343.474618407

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..799

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A001611(n+1).

Row 1 is A000045(n+1).

Row 2 is A003229(n-1) for n>2.

Formula

Empirical for column k:

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

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

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

k=4: a(n) = a(n-1) +2*a(n-2) -a(n-4) for n>8

k=5: a(n) = a(n-1) +3*a(n-3) +2*a(n-4) +2*a(n-5) for n>10

k=6: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +a(n-4) -2*a(n-5) -a(n-6) for n>12

k=7: [order 12] for n>19

Empirical for row n:

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

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

n=3: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) for n>7

n=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +5*a(n-4) -3*a(n-5) -3*a(n-6) +2*a(n-7) for n>11

n=5: [order 11] for n>16

n=6: [order 17] for n>23

n=7: [order 31] for n>38