A348009 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.

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

Offset: 0

Author

Scott R. Shannon, Sep 24 2021

Keywords

• nonn
• walk

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A347990 (four quadrants), A348008 (two quadrants), A038373, A001411, A337353.