A304065 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 14, 18, 0, 0, 61, 69, 69, 61, 0, 0, 209, 376, 661, 376, 209, 0, 0, 702, 1891, 5580, 5580, 1891, 702, 0, 0, 2381, 9889, 48148, 79185, 48148, 9889, 2381, 0, 0, 8069, 51283, 418382, 1105513, 1105513, 418382, 51283, 8069, 0, 0, 27330

Offset

1,5

Comments

Table starts

.0....0......0........0..........0............0..............0................0

.0....3......5.......18.........61..........209............702.............2381

.0....5.....14.......69........376.........1891...........9889............51283

.0...18.....69......661.......5580........48148.........418382..........3621421

.0...61....376.....5580......79185......1105513.......15790468........223280583

.0..209...1891....48148....1105513.....25507453......598203550......13909028356

.0..702...9889...418382...15790468....598203550....23106300531.....882586820005

.0.2381..51283..3621421..223280583..13909028356...882586820005...55351295222420

.0.8069.265582.31403562.3167599806.324563218021.33883349300951.3491582407808941

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6

k=3: [order 14] for n>16

k=4: [order 42] for n>43

Example

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

Crossrefs

Column 2 is A303684.

Sequence in context: A305509 A305175 A316763 * A305457 A305022 A316686

Adjacent sequences: A304062 A304063 A304064 * A304066 A304067 A304068

Keyword

nonn,tabl

Author

R. H. Hardin, May 05 2018

Status

approved