A300435 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 2, 1, 2, 6, 6, 2, 3, 15, 13, 15, 3, 5, 37, 33, 33, 37, 5, 8, 90, 87, 87, 87, 90, 8, 13, 223, 228, 238, 238, 228, 223, 13, 21, 550, 611, 697, 704, 697, 611, 550, 21, 34, 1355, 1656, 1942, 2104, 2104, 1942, 1656, 1355, 34, 55, 3341, 4479, 5656, 6235, 6677, 6235

Offset

1,5

Comments

Table starts

..0....1....1.....2.....3......5......8......13.......21.......34........55

..1....2....6....15....37.....90....223.....550.....1355.....3341......8237

..1....6...13....33....87....228....611....1656.....4479....12100.....32579

..2...15...33....87...238....697...1942....5656....16487....48053....140187

..3...37...87...238...704...2104...6235...18461....54864...165251....497102

..5...90..228...697..2104...6677..21891...68080...218474...707211...2281943

..8..223..611..1942..6235..21891..75553..267811...932791..3315683..11885340

.13..550.1656..5656.18461..68080.267811.1012416..3997806.15519340..61763490

.21.1355.4479.16487.54864.218474.932791.3997806.16998387.73709560.320416260

Links

R. H. Hardin, Table of n, a(n) for n = 1..263

Formula

Empirical for column k:

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

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

k=3: [order 31]

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A300344.

Sequence in context: A324342 A140835 A300350 * A300769 A300639 A301361

Adjacent sequences: A300432 A300433 A300434 * A300436 A300437 A300438

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 05 2018

Status

approved