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A297375
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Number of 2 X n 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0, 1 or 2 neighboring 1s.
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1
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4, 16, 57, 208, 765, 2807, 10294, 37759, 138506, 508054, 1863591, 6835838, 25074539, 91975917, 337376860, 1237532061, 4539391360, 16650941468, 61077318469, 224037712140, 821792732873, 3014417927011, 11057186411122, 40558865522523
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