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A300259
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
5
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, 1588195, 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.....1588195......24735890........385299869
..32...1841...40023....974646....24735890.....618957455......15475106013
..64...7181..243312...9424684...385299869...15475106013.....620657860617
.128..28010.1479656..91234133..6015414147..388173584774...24999315059414
.256.109255.8997567.882982660.93883095950.9733989458695.1006615871837972
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..1..1..1. .0..0..1..0. .0..0..1..0. .0..1..0..1. .0..1..1..0
..0..1..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..0. .0..0..1..0
..1..1..0..1. .1..0..1..1. .1..0..0..1. .1..0..0..0. .1..0..1..1
..0..0..0..1. .1..0..0..1. .1..0..0..0. .1..0..1..1. .0..1..1..0
..1..1..0..1. .0..0..1..1. .1..0..1..0. .1..1..0..1. .0..0..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A281831.
Column 3 is A299663.
Column 4 is A299664.
Sequence in context: A299001 A299746 A299668 * A305523 A298970 A316960
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 01 2018
STATUS
approved