

A335098


The number of constructible vertically balanced selfavoiding walks of length n on the upper halfplane of a 2D square lattice where the nodes and connecting rods have equal mass.


0



3, 5, 11, 23, 51, 109, 251, 549, 1291, 2981, 7067, 16571, 39601, 94195, 226997, 544687, 1320935, 3194399, 7797891, 18996977, 46651387, 114353905, 282109663, 694793903, 1720327219, 4253521985, 10565387267, 26213565665, 65300013637, 162516950805, 405892537979
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OFFSET

1,1


COMMENTS

This is a variation of A337860 where at every step, given the nodes and connecting rods have equal mass, the resulting 2D lattice structure is stable against toppling, assuming no sideways perturbations. See that sequence for further details of the allowed walks.


LINKS

Table of n, a(n) for n=1..31.


EXAMPLE

a(1) = 3, a(2) = 5. These are the same stable walks as in A337860.
a(3) = 11. The constructible stable walks given a first step to the right are:
.
+
+ ++ ++ 
   +
X+++ X++ X+ X+ 
X+
.
These walks can also take a first step to the left thus, along with the directly vertical walk, the total number of stable walks is 2*5 + 1 = 11.
One 3step walk which is not counted here, along with its parent 2step walk, is:
.
++ ++
 ==>  
X X +
.
After two steps the resulting structure is not stable against toppling, its centerofmass is clearly to the right of the one node at y=0, thus any resulting 3step walks resulting from this unstable 2step walk are not counted.


CROSSREFS

Cf. A337860, A337317, A335780, A337761, A116903, A116904, A001411.
Sequence in context: A246491 A084361 A077229 * A018113 A113281 A037446
Adjacent sequences: A335095 A335096 A335097 * A335099 A335100 A335101


KEYWORD

nonn,walk


AUTHOR

Scott R. Shannon, Sep 12 2020


STATUS

approved



