A335596 The number of hanging vertically stable self-avoiding walks of length n on a 2D square lattice where only the connecting rods have mass.

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

Offset: 1

Author

Scott R. Shannon, Sep 13 2020

Keywords

• nonn
• walk
• more

Comments

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.

Examples

			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:
.
            X-----+
                  |
                  |
+-----+-----+-----+
,
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.
		

Crossrefs

Cf. A335780 (rods and nodes have mass), A335307 (only nodes have mass), A116903, A337761, A001411, A001412.