A305457 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 5 or 8 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, 79810, 48148, 9889, 2381, 0, 0, 8069, 51283, 418382, 1117343, 1117343, 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......79810......1117343.......16062787........228184784

.0..209...1891....48148....1117343.....25891309......612656116......14339915102

.0..702...9889...418382...16062787....612656116....23996865179.....926180069711

.0.2381..51283..3621421..228184784..14339915102...926180069711...58862515324951

.0.8069.265582.31403562.3255027240.337239061289.35989846262523.3770741435617783

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..1..0..1. .0..0..0..1. .0..0..1..1. .0..0..1..0. .0..1..0..1
..1..1..1..0. .1..1..0..1. .1..1..0..0. .1..1..1..1. .1..0..1..0
..0..0..0..1. .1..0..1..1. .0..1..0..0. .0..0..0..1. .0..1..1..0
..1..0..0..0. .0..0..0..1. .1..1..1..1. .1..1..0..0. .1..0..0..1
..0..1..0..1. .1..1..0..1. .0..0..0..0. .0..1..1..1. .0..1..0..1

Crossrefs

Column 2 is A303684.

Column 3 is A304060.

Column 4 is A304061.

Sequence in context: A305175 A316763 A304065 * A305022 A316686 A304767

Adjacent sequences: A305454 A305455 A305456 * A305458 A305459 A305460

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 01 2018

Status

approved