login
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.
7
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 15 2018
STATUS
approved