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A348009
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Number of n-step self-avoiding walks on one quadrant of a 2D square lattice where the walk cannot step to the smaller square ring of numbers than the ring it is currently on.
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1
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1, 2, 4, 10, 22, 52, 118, 282, 646, 1544, 3576, 8546, 19924, 47612, 111536, 266488, 626520, 1496670, 3528470, 8427952, 19913078, 47559756, 112572916, 268857568, 637327742, 1522153378, 3612811784, 8629110414, 20503211908, 48975965026, 116478744692
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OFFSET
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0,2
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COMMENTS
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This is a variation of A347990. The same walk rules apply except that the walk is confined to one quadrant of the 2D square lattice. See A347990 for further details.
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LINKS
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EXAMPLE
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a(0..3) are the same as the standard SAW on one quadrant of a square lattice, see A038373, as the walk cannot step to a smaller ring in the first three steps.
a(4) = 22. If we restrict the first one or more steps to the right followed by an upward step then there is one walk which steps to a smaller ring and is thus forbidden. That is the walk (0,0) -> (1,0) -> (2,0) -> (2,1) -> (1,1). As this can be walked in two different ways in one quadrant the number of 4-step walks becomes A038373(4) - 2 = 24 - 2 = 22.
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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