Circular (bracelets) permutations with alike things(reflections are equivalent) using polya enumeration

Circular permutations of N objects of n1 are identical of one type, n2 are identical of another type and so on, such that n1+n2+n3+….. = N? A similar question exists but it doesn’t address the case where reflections are under the same equivalent class.$ $ \frac{1}{N}\sum_{d | N} \phi(d) p_d^{N/d}$ $ This is when reflections are not the same. How does the equation change under this new restriction.

Note: I couldn’t comment on that question due to my low reputation, so I made this question.

Term for an A*-like pathfinding strategy where only the heuristic goal distance matters

I am trying to find a proper term for the A*-like best-first pathfinding strategy where the node to expand next is the one with the least estimated distance from the goal, regardless of its distance from the source.

In best-first search algorithms, the node to expand next is the most promising one according to some evaluation function (which may take into account the current global knowledge). In the normal A* algorithm, the evaluation function is the sum of the length of the currently know shortest path from the source and the heuristic estimate of the distance to the goal. Is there a standard term for a similar strategy where the evaluation function is just the heuristic distance to the goal?

I was thinking about greedy and hill-climbing, but greedy in this context seems to be just a synonym of best-first, and in what is commonly referred to as hill-climbing, there seems to be either no backtracking, or just one-step backtracking, that is, old unexpanded nodes are discarded at each step.