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A299602 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero. 7
0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 6, 9, 6, 0, 0, 17, 27, 27, 17, 0, 0, 41, 147, 130, 147, 41, 0, 0, 104, 643, 1241, 1241, 643, 104, 0, 0, 261, 3051, 8825, 21367, 8825, 3051, 261, 0, 0, 655, 14539, 72751, 290941, 290941, 72751, 14539, 655, 0, 0, 1646, 69087, 589816, 4309263 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,8
COMMENTS
Table starts
.0...0.....0.......0.........0............0..............0................0
.0...1.....3.......6........17...........41............104..............261
.0...3.....9......27.......147..........643...........3051............14539
.0...6....27.....130......1241.........8825..........72751...........589816
.0..17...147....1241.....21367.......290941........4309263.........63960652
.0..41...643....8825....290941......7242300......197267780.......5361395737
.0.104..3051...72751...4309263....197267780.....9743385598.....481541186894
.0.261.14539..589816..63960652...5361395737...481541186894...43313516068423
.0.655.69087.4803248.948323066.145483752329.23753464370841.3889298014550366
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) +2*a(n-3)
k=3: [order 13] for n>15
k=4: [order 48]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..1..1..1. .1..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0
..0..1..1..1. .1..1..0..0. .0..0..1..1. .0..0..0..0. .1..0..0..1
..0..0..1..1. .1..1..1..0. .0..0..0..1. .0..0..0..0. .1..1..1..1
CROSSREFS
Column 2 is A297972.
Sequence in context: A299334 A268759 A298841 * A299554 A300175 A129533
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 14 2018
STATUS
approved

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Last modified April 13 15:44 EDT 2024. Contains 371644 sequences. (Running on oeis4.)