A300539 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 16, 12, 16, 1, 1, 40, 36, 36, 40, 1, 1, 113, 122, 300, 122, 113, 1, 1, 304, 429, 1436, 1436, 429, 304, 1, 1, 833, 1585, 8974, 12951, 8974, 1585, 833, 1, 1, 2270, 5755, 52012, 124543, 124543, 52012, 5755, 2270, 1, 1, 6194, 21084, 311037

Offset

1,5

Comments

Table starts

.1....1.....1.......1.........1..........1............1..............1

.1....3.....5......16........40........113..........304............833

.1....5....12......36.......122........429.........1585...........5755

.1...16....36.....300......1436.......8974........52012.........311037

.1...40...122....1436.....12951.....124543......1220365.......11917710

.1..113...429....8974....124543....1972991.....31434011......501719570

.1..304..1585...52012...1220365...31434011....831752031....21825406629

.1..833..5755..311037..11917710..501719570..21825406629...946782030618

.1.2270.21084.1845926.117661891.8058860856.577067248097.41212879288810

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +4*a(n-2) +2*a(n-3) -a(n-6)

k=3: [order 22] for n>24

k=4: [order 75] for n>78

Example

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

Crossrefs

Sequence in context: A176481 A108553 A176700 * A300966 A300923 A301531

Adjacent sequences: A300536 A300537 A300538 * A300540 A300541 A300542

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 08 2018

Status

approved