A301790 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 4, 5, 6, 13, 8, 8, 9, 12, 34, 16, 13, 14, 17, 24, 89, 32, 21, 22, 25, 32, 48, 233, 64, 34, 35, 38, 45, 61, 96, 610, 128, 55, 56, 59, 66, 82, 116, 192, 1597, 256, 89, 90, 93, 100, 116, 150, 221, 384, 4181, 512, 144, 145, 148, 155, 171, 205, 275, 421, 768, 10946

Offset: 1

Author

R. H. Hardin, Mar 26 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1....2...3...5...8...13...21...34...55...89..144...233...377...610...987

...2....5...6...9..14...22...35...56...90..145..234...378...611...988..1598

...4...13..12..17..25...38...59...93..148..237..381...614...991..1601..2588

...8...34..24..32..45...66..100..155..244..388..621...998..1608..2595..4192

..16...89..48..61..82..116..171..260..404..637.1014..1624..2611..4208..6792

..32..233..96.116.150..205..294..438..671.1048.1658..2645..4242..6826.11007

..64..610.192.221.275..364..508..741.1118.1728.2715..4312..6896.11077.17842

.128.1597.384.421.505..648..881.1258.1868.2855.4452..7036.11217.17982.28928

.256.4181.768.802.928.1156.1532.2142.3129.4726.7310.11491.18256.29202.46913

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1920

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A001519(n+1).

Column 3 is A003945.

Row 1 is A000045(n+1).

Formula

Empirical for column k:

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

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

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

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

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

k=6: a(n) = a(n-1) +2*a(n-2) -a(n-4) -a(n-5) -a(n-6)

k=7: a(n) = 2*a(n-1) -a(n-4) -a(n-6)

Empirical for row n:

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

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

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

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

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

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

n=7: a(n) = 2*a(n-1) -a(n-3) for n>7