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A300923 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 16, 20, 16, 1, 1, 40, 76, 76, 40, 1, 1, 113, 290, 593, 290, 113, 1, 1, 304, 1245, 4066, 4066, 1245, 304, 1, 1, 833, 5160, 30474, 48588, 30474, 5160, 833, 1, 1, 2270, 21819, 224767, 640673, 640673, 224767, 21819, 2270, 1, 1, 6194, 91713 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
.1....1.....1........1..........1............1..............1................1
.1....3.....5.......16.........40..........113............304..............833
.1....5....20.......76........290.........1245...........5160............21819
.1...16....76......593.......4066........30474.........224767..........1677576
.1...40...290.....4066......48588.......640673........8265835........108469760
.1..113..1245....30474.....640673.....14914968......340365586.......7878577344
.1..304..5160...224767....8265835....340365586....13715723327.....560932609225
.1..833.21819..1677576..108469760...7878577344...560932609225...40555879417852
.1.2270.91713.12501697.1419225976.181974865532.22881004568048.2924437698122344
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +4*a(n-2) +2*a(n-3) -a(n-6)
k=3: [order 21] for n>22
k=4: [order 66] for n>68
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..1. .0..0..0..0
..0..1..1..1. .1..1..0..0. .0..0..0..0. .0..1..0..0. .0..0..1..0
..1..1..1..1. .1..1..0..0. .0..1..0..1. .0..0..0..1. .0..0..0..1
..0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0. .0..0..1..1
..0..1..0..0. .0..1..1..0. .1..1..0..0. .0..1..0..1. .0..0..1..0
CROSSREFS
Column 2 is A300533.
Sequence in context: A176700 A300539 A300966 * A301531 A158418 A124925
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 15 2018
STATUS
approved

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Last modified April 21 03:36 EDT 2024. Contains 371850 sequences. (Running on oeis4.)