A348008 Number of n-step self-avoiding walks on the upper two quadrants 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, 3, 7, 19, 45, 115, 273, 683, 1629, 4035, 9643, 23713, 56761, 138883, 332807, 811343, 1945777, 4730655, 11351999, 27542291, 66123953, 160174529, 384700337, 930720767, 2236106651, 5404679299, 12988762401, 31370201873, 75409375419, 182019777165, 437648513199

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 the upper two quadrants of the 2D square lattice. See A347990 for further details.

Examples

			a(0..3) are the same as the standard SAW on the upper two quadrants of a square lattice, see A116903, as the walk cannot step to a smaller ring in the first three steps.
a(4) = 45. 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 four different ways in the upper two quadrants the number of 4-step walks becomes A116903(4) - 4 = 49 - 4 = 45.
		

Crossrefs

Cf. A347990 (four quadrants), A348009 (one quadrant), A116903, A001411, A337353.