A335098 The number of constructible vertically balanced self-avoiding walks of length n on the upper half-plane of a 2D square lattice where the nodes and connecting rods have equal mass.

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

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 3-step walk which is not counted here, along with its parent 2-step walk, is:
.
+---+        +---+
|      ==>   |   |
X            X   +
.
After two steps the resulting structure is not stable against toppling, its center-of-mass is clearly to the right of the one node at y=0, thus any resulting 3-step walks resulting from this unstable 2-step 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