Sequence for sum of adjacent two number is all square number

main.py

from collections import defaultdict
from typing import Optional


def hamilton(G: dict[int, list[int]], size: int, pt: int, path: Optional[list] = None) -> Optional[list[int]]:
    if not path:
        path = []
    # print('hamilton called with pt={}, path={}'.format(pt, path))
    if pt not in path:
        path.append(pt)
        if len(path)==size and issquare( path[0] + path[-1]):
            print(path)
            return path
        for pt_next in G.get(pt):
            res_path = [i for i in path]
            candidate = hamilton(G, size, pt_next, res_path)
            if candidate is not None:  # skip loop or dead end
                return candidate
        # print('path {} is a dead end'.format(path))
    else:
        # print('pt {} already in path {}'.format(pt, path))
        return
    # loop or dead end, None is implicitly returned


def make_graph(max: int) -> dict[int, list[int]]:
    graph = defaultdict(list)
    for i in range(1, max + 1):
        for j in range(1, max +1):
            if i != j and issquare(i + j):
                graph[i].append(j)
    return graph


def issquare(n:int) -> bool:
    return int(n ** 0.5) ** 2 == n


if __name__ == "__main__":
    max_number = 32
    for i in range (1, max_number + 1):
        g = make_graph(max_number)
        hamilton(g, max_number, i)