login
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, 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
1,5
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.
EXAMPLE
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.
Sequence in context: A363142 A191627 A178778 * A238824 A340766 A161943
KEYWORD
nonn,walk,more
AUTHOR
Scott R. Shannon, Sep 13 2020
STATUS
approved