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A335596
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The number of hanging vertically stable self-avoiding walks of length n on a 2D square lattice where only the connecting rods have mass.
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1
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1, 1, 1, 1, 3, 7, 17, 43, 91, 183, 371, 799, 1941, 4621, 11463, 27823, 68997, 167481, 414045, 1006091, 2496981, 6127053, 15304071, 37838777, 95041475, 236320611, 595206771
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OFFSET
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1,5
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COMMENTS
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This is a variation of A335780 where only the rods between the nodes have mass. See that sequence for further details of the allowed walks.
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LINKS
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EXAMPLE
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a(1)-a(4) = 1 as the only stable walk is a walk straight down from the first node.
a(5) = 3. There is one stable walk with a first step to the right:
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+-----+-----+-----+
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Assuming a rod mass of q, the total torque to the right of the first node is 2*q*(1/2) + 1*q*1 = 2q. The total torque to the left of the first node is 1*q*(1/2) + 1*q*(3/2) = 2q. This walk can be taken in 2 ways. Thus, with the straight down walk, the total number of stable walks is 2+1 = 3.
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CROSSREFS
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KEYWORD
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nonn,walk,more
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AUTHOR
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STATUS
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approved
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