A305482 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 31, 21, 21, 31, 13, 21, 49, 40, 48, 40, 49, 21, 34, 103, 70, 98, 98, 70, 103, 34, 55, 193, 125, 192, 277, 192, 125, 193, 55, 89, 327, 231, 368, 577, 577, 368, 231, 327, 89, 144, 641, 419, 732, 1245, 1558, 1245, 732, 419, 641

Offset

1,2

Comments

Table starts

..1...2...3....5....8....13.....21.....34......55......89......144.......233

..2...5...7...17...31....49....103....193.....327.....641.....1207......2129

..3...7..10...21...40....70....125....231.....419.....752.....1365......2482

..5..17..21...48...98...192....368....732....1480....2932.....5776.....11486

..8..31..40...98..277...577...1245...2868....6381...14206....31630.....70391

.13..49..70..192..577..1558...3910..10465...27679...70960...185085....482009

.21.103.125..368.1245..3910..11438..34687..106558..317866...952180...2866802

.34.193.231..732.2868.10465..34687.123104..440388.1501195..5216253..18221847

.55.327.419.1480.6381.27679.106558.440388.1894686.7620015.31132355.129187191

Links

R. H. Hardin, Table of n, a(n) for n = 1..420

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +3*a(n-3) -2*a(n-6) for n>9

k=4: [order 10] for n>13

k=5: [order 29] for n>33

k=6: [order 60] for n>66

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303677.

Sequence in context: A304544 A306129 A304221 * A305252 A316552 A316311

Adjacent sequences: A305479 A305480 A305481 * A305483 A305484 A305485

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 02 2018

Status

approved