This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335596 #13 Oct 14 2020 23:15:49 %S A335596 1,1,1,1,3,7,17,43,91,183,371,799,1941,4621,11463,27823,68997,167481, %T A335596 414045,1006091,2496981,6127053,15304071,37838777,95041475,236320611, %U A335596 595206771 %N 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. %C A335596 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. %e A335596 a(1)-a(4) = 1 as the only stable walk is a walk straight down from the first node. %e A335596 a(5) = 3. There is one stable walk with a first step to the right: %e A335596 . %e A335596 X-----+ %e A335596 | %e A335596 | %e A335596 +-----+-----+-----+ %e A335596 , %e A335596 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. %Y A335596 Cf. A335780 (rods and nodes have mass), A335307 (only nodes have mass), A116903, A337761, A001411, A001412. %K A335596 nonn,walk,more %O A335596 1,5 %A A335596 _Scott R. Shannon_, Sep 13 2020