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A302381 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
0, 1, 0, 1, 3, 0, 2, 15, 11, 0, 3, 46, 76, 34, 0, 5, 161, 430, 475, 111, 0, 8, 601, 2886, 4640, 2771, 361, 0, 13, 2208, 19215, 56541, 48980, 16451, 1172, 0, 21, 8053, 127535, 688999, 1089035, 514655, 97160, 3809, 0, 34, 29415, 847604, 8334338, 24209608, 20993054 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
.0.....1.......1.........2............3..............5................8
.0.....3......15........46..........161............601.............2208
.0....11......76.......430.........2886..........19215...........127535
.0....34.....475......4640........56541.........688999..........8334338
.0...111....2771.....48980......1089035.......24209608........535192095
.0...361...16451....514655.....20993054......849467774......34271733937
.0..1172...97160...5421003....404225195....29810775827....2195619257236
.0..3809..574671..57068484...7787623959..1046322460741..140685735128595
.0.12377.3397622.600825641.150008013842.36721875744312.9013655138528774
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 11]
k=4: [order 26]
k=5: [order 84] for n>86
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4) for n>5
n=3: [order 14] for n>15
n=4: [order 42] for n>43
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..1..0..0. .0..1..1..0. .0..0..0..0. .0..1..1..1
..0..1..1..0. .0..0..1..0. .0..0..0..1. .0..0..1..1. .1..0..0..0
..0..1..1..1. .0..0..1..1. .0..1..1..1. .0..0..1..0. .0..1..0..0
..1..0..1..0. .0..0..1..1. .0..0..0..0. .0..1..0..0. .0..0..1..1
..1..1..0..0. .0..1..1..1. .0..0..1..1. .1..1..0..0. .1..1..0..0
CROSSREFS
Column 2 is A180762.
Row 1 is A000045(n-1).
Row 2 is A232077(n-1).
Sequence in context: A302472 A303254 A256068 * A303102 A302953 A350464
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 06 2018
STATUS
approved

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Last modified October 2 11:37 EDT 2023. Contains 365833 sequences. (Running on oeis4.)