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A228277
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Number of n X n binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or nw-se diagonally.
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11
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1, 1, 13, 133, 3631, 172082, 16566199, 3057290265, 1105411581741, 776531523355217, 1063228770141145384, 2834013489992345694498, 14712337761578682394367473, 148727865257442275211424889367
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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No known recurrence.
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EXAMPLE
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The thirteen solutions for n=3 correspond to the thirteen possible values of 5-bit numbers with no two adjacent bits equal to 1, namely, the matrices
( 1 0 a )
( 0 0 b )
( e d c ) ; with abcde = A014417(0,...,12) = 0, 1, 10, 100, 101, 1000, 1001, 1010, 10000, 10001, 10010, 10100, 10101 (leading zeros omitted). - M. F. Hasler, Apr 27 2014
Some solutions for n=4:
.1..0..0..1. .1..0..0..0. .1..0..0..0. .1..0..0..0. .1..0..0..0
.0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..0. .0..0..0..0
.0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1
.1..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..0. .0..0..1..0
The last example shows that sw-ne (= anti)diagonally adjacent "1"s are allowed. See A228476, A228506 and A228390 for other variants.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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