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A302808 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
1, 2, 2, 4, 8, 4, 8, 29, 32, 8, 16, 105, 169, 128, 16, 32, 384, 934, 1010, 512, 32, 64, 1405, 5117, 8718, 6084, 2048, 64, 128, 5135, 28128, 74072, 82367, 36456, 8192, 128, 256, 18766, 154494, 632004, 1089773, 773520, 218640, 32768, 256, 512, 68589, 848519 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1......2.......4.........8..........16............32..............64
...2......8......29.......105.........384..........1405............5135
...4.....32.....169.......934........5117.........28128..........154494
...8....128....1010......8718.......74072........632004.........5396562
..16....512....6084.....82367.....1089773......14458177.......192211013
..32...2048...36456....773520....15904814.....327603711......6769884156
..64...8192..218640...7267160...232260380....7428713676....238687785290
.128..32768.1312416..68346451..3396923500..168777255305...8434497360938
.256.131072.7873344.642498696.49653502029.3832039683236.297820640670676
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 6*a(n-1) +24*a(n-3) -144*a(n-4) for n>6
k=4: [order 18] for n>20
k=5: [order 90] for n>92
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
n=3: [order 13] for n>15
n=4: [order 48] for n>50
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..0. .0..1..1..0
..1..0..1..1. .0..1..1..0. .1..0..1..0. .0..0..1..1. .1..1..1..1
..1..0..1..0. .0..1..0..1. .1..0..1..1. .0..0..1..1. .0..0..0..0
..0..1..0..1. .0..0..0..0. .1..0..0..0. .1..0..1..1. .0..1..1..0
..1..1..0..0. .0..0..1..1. .1..0..1..0. .1..0..1..0. .1..1..1..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Row 1 is A000079(n-1).
Row 2 is A302266.
Sequence in context: A301450 A302265 A302965 * A303469 A281955 A316183
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 13 2018
STATUS
approved

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Last modified June 16 22:16 EDT 2024. Contains 373432 sequences. (Running on oeis4.)