A335307 The number of hanging vertically stable self-avoiding walks of length n on a 2D square lattice where only the nodes have mass.

1, 1, 1, 1, 5, 13, 31, 63, 141, 293, 665, 1553, 3795, 9225, 22257, 53623, 132277, 321651, 786553, 1928565, 4806503, 11885969, 29498995, 73362933, 184210629, 460165983, 1151961103

Offset

1,5

Comments

This is a variation of A335780 where only the nodes have mass. See that sequence for further details of the allowed walks.

Links

Table of n, a(n) for n=1..27.

Example

a(1)-a(4) = 1 as the only stable walk is a walk straight down from the first node.
a(5) = 5. There are two stable walks with a first step to the right:
.
      X-----+
            |     +     X-----+
            |     |           |
+-----+-----+     |           |
|                 +-----+-----+
|
+
.
Assuming a node mass of p, both walks have a torque of 2p to the right and 2p to the left of the first node. These walks can be taken in 2 ways. Thus, with the straight down walk, the total number of stable walks is 2*2+1 = 5.

Crossrefs

Cf. A335780 (rods and nodes have mass), A335596 (only rods have mass), A116903, A337761, A001411, A001412.

Sequence in context: A165888 A021007 A109419 * A067333 A369176 A209009

Adjacent sequences: A335304 A335305 A335306 * A335308 A335309 A335310

Keyword

nonn,walk,more

Author

Scott R. Shannon, Sep 12 2020

Status

approved