For n=2, the a(2) = 3 solutions visit one of the three vertices adjacent to the initial vertex, and then return.
For n=5, the a(5) = 6 solutions consist of counterclockwise or clockwise traversals of the circumference of any of the three pentagons that surround the initial vertex.
CROSSREFS
The accompanying sequences for the number of paths that return to a degree-4 node is A357810.
Similar sequences for square, hexagonal, and honeycomb lattices are A002894, A002898 and A002893.
