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A303102 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
0, 1, 0, 1, 3, 0, 2, 15, 11, 0, 3, 46, 77, 34, 0, 5, 161, 431, 486, 111, 0, 8, 601, 2913, 4667, 2869, 361, 0, 13, 2208, 19393, 58160, 49534, 17229, 1172, 0, 21, 8053, 128921, 709333, 1138331, 523578, 102952, 3809, 0, 34, 29415, 857789, 8650205, 25372284, 22292709 (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......77.......431.........2913..........19393............128921
.0....34.....486......4667........58160.........709333...........8650205
.0...111....2869.....49534......1138331.......25372284.........568099880
.0...361...17229....523578.....22292709......906385523.......37220475492
.0..1172..102952...5550469....436394066....32409609245.....2441756629583
.0..3809..616065..58797885...8545589681..1158734336743...160164698180399
.0.12377.3685099.622939052.167325743073.41428642572259.10505922762123798
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 90] for n>91
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..1..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0. .0..1..0..1
..1..0..1..0. .1..1..1..1. .1..1..0..0. .0..1..1..1. .0..0..1..0
..1..0..0..1. .0..0..0..1. .1..1..1..1. .0..0..1..0. .1..0..0..0
..0..1..1..0. .0..1..1..0. .0..0..0..0. .0..1..0..1. .0..1..1..1
..1..1..0..0. .1..1..0..0. .1..1..1..1. .1..0..1..0. .1..0..0..0
CROSSREFS
Column 2 is A180762.
Row 1 is A000045(n-1).
Row 2 is A232077(n-1).
Sequence in context: A303254 A256068 A302381 * A302953 A350464 A247706
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 18 2018
STATUS
approved

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Last modified February 26 05:55 EST 2024. Contains 370335 sequences. (Running on oeis4.)