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A302623
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 4, 8, 4, 8, 17, 25, 8, 16, 37, 25, 81, 16, 32, 78, 45, 71, 264, 32, 64, 169, 79, 130, 191, 857, 64, 128, 361, 146, 251, 367, 498, 2785, 128, 256, 778, 286, 497, 896, 917, 1321, 9050, 256, 512, 1673, 563, 1051, 2229, 2669, 2533, 3505, 29407, 512, 1024, 3605
OFFSET
1,2
COMMENTS
Table starts
...1.....2....4.....8....16.....32......64......128.......256........512
...2.....8...17....37....78....169.....361......778......1673.......3605
...4....25...25....45....79....146.....286......563......1114.......2222
...8....81...71...130...251....497....1051.....2274......4999......10972
..16...264..191...367...896...2229....5771....15303.....41564.....113363
..32...857..498...917..2669...9015...30536...106951....390471....1418770
..64..2785.1321..2533..8283..36510..159831...722300...3485735...16654024
.128..9050.3505..6871.25770.150072..851266..5004858..32283797..204853561
.256.29407.9240.18334.79047.606756.4471550.34111427.294788397.2490596189
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 9] for n>11
k=4: [order 8] for n>10
k=5: [order 15] for n>20
k=6: [order 21] for n>27
k=7: [order 35] for n>43
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) -2*a(n-4) +4*a(n-5) for n>6
n=3: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) for n>8
n=4: [order 8] for n>11
n=5: [order 16] for n>21
n=6: [order 29] for n>35
n=7: [order 51] for n>62
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..0. .0..1..0..1. .0..0..1..0. .0..1..0..0
..1..0..1..0. .0..0..1..0. .0..1..0..1. .1..0..1..0. .1..1..0..1
..1..0..1..0. .1..0..1..0. .0..1..1..1. .1..0..1..0. .1..0..0..1
..0..1..0..1. .0..0..1..1. .0..1..0..1. .1..1..1..0. .1..0..1..1
..0..1..0..1. .1..1..0..0. .0..1..0..1. .1..0..1..1. .0..0..1..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240478.
Row 1 is A000079(n-1).
Row 2 is A281470.
Sequence in context: A183397 A339490 A281469 * A302415 A303182 A302322
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 10 2018
STATUS
approved