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A300539 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 8
1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 16, 12, 16, 1, 1, 40, 36, 36, 40, 1, 1, 113, 122, 300, 122, 113, 1, 1, 304, 429, 1436, 1436, 429, 304, 1, 1, 833, 1585, 8974, 12951, 8974, 1585, 833, 1, 1, 2270, 5755, 52012, 124543, 124543, 52012, 5755, 2270, 1, 1, 6194, 21084, 311037 (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....12......36.......122........429.........1585...........5755
.1...16....36.....300......1436.......8974........52012.........311037
.1...40...122....1436.....12951.....124543......1220365.......11917710
.1..113...429....8974....124543....1972991.....31434011......501719570
.1..304..1585...52012...1220365...31434011....831752031....21825406629
.1..833..5755..311037..11917710..501719570..21825406629...946782030618
.1.2270.21084.1845926.117661891.8058860856.577067248097.41212879288810
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 22] for n>24
k=4: [order 75] for n>78
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..0. .0..0..0..0. .0..1..1..0. .0..1..1..0
..1..1..0..0. .1..1..0..1. .0..1..1..0. .1..1..1..1. .1..0..1..1
..1..1..1..1. .0..1..1..1. .0..1..0..0. .0..0..1..1. .1..1..1..1
..0..1..0..1. .1..1..0..1. .0..0..1..0. .0..0..1..0. .0..0..0..1
..1..1..1..0. .0..1..1..1. .0..0..0..1. .0..0..0..0. .0..0..1..1
CROSSREFS
Sequence in context: A176481 A108553 A176700 * A300966 A300923 A301531
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 08 2018
STATUS
approved

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Last modified June 14 23:20 EDT 2024. Contains 373401 sequences. (Running on oeis4.)