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Let's say from your first node (D) you go to (A). From there you have 5 choices, not 7 (B, F, E, H, G).
I don't understand the test case count_patterns_from("D", 3) == 37.
Starting from node "D", we can choose seven following nodes, as only node "F" is blocked from "D". From any follow-up node, using the retracing rule, we can reach any other node, for a total of seven further follow-ups.
This totals up to 7x7 = 49 paths, which is greater than the reference 37. Am I getting the rules wrong?
Nice kata, thank's guys!