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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A001519(n+1).

Column 3 is A003945.

Row 1 is A000045(n+1).

Sequence in context: A210212 A209762 A026408 * A301964 A334043 A301884

Adjacent sequences: A301787 A301788 A301789 * A301791 A301792 A301793

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 26 2018

Status

approved