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
Examples
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.
Comments