A299668 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 31, 31, 8, 16, 121, 179, 121, 16, 32, 472, 1080, 1080, 472, 32, 64, 1841, 6585, 10363, 6585, 1841, 64, 128, 7181, 40023, 100823, 100823, 40023, 7181, 128, 256, 28010, 243312, 974646, 1585983, 974646, 243312, 28010, 256, 512, 109255, 1479656

Offset

1,2

Comments

Table starts

...1......2.......4.........8..........16............32..............64

...2......8......31.......121.........472..........1841............7181

...4.....31.....179......1080........6585.........40023..........243312

...8....121....1080.....10363......100823........974646.........9424684

..16....472....6585....100823.....1585983......24665530.......383819990

..32...1841...40023....974646....24665530.....615314145.....15351583824

..64...7181..243312...9424684...383819990...15351583824....613943466291

.128..28010.1479656..91234133..5986258088..384274120067..24660009931840

.256.109255.8997567.882982660.93328306577.9615094296606.990036737595402

Links

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

Formula

Empirical for column k:

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

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

k=3: [order 11] for n>12

k=4: [order 38] for n>39

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281831.

Sequence in context: A299844 A299001 A299746 * A300259 A305523 A298970

Adjacent sequences: A299665 A299666 A299667 * A299669 A299670 A299671

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 15 2018

Status

approved