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

1,2

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

Links

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

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

Example

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

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.

Sequence in context: A136537 A153928 A119446 * A302515 A303314 A349122

Adjacent sequences: A302677 A302678 A302679 * A302681 A302682 A302683

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 11 2018

Status

approved