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%I #5 Oct 11 2021 18:56:05
%S 1,2,4,10,22,52,118,282,646,1544,3576,8546,19924,47612,111536,266488,
%T 626520,1496670,3528470,8427952,19913078,47559756,112572916,268857568,
%U 637327742,1522153378,3612811784,8629110414,20503211908,48975965026,116478744692
%N 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.
%C 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.
%e 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.
%e 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.
%Y Cf. A347990 (four quadrants), A348008 (two quadrants), A038373, A001411, A337353.
%K nonn,walk
%O 0,2
%A _Scott R. Shannon_, Sep 24 2021
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