Combinations for Screen lock For iPhone / Android

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I was wondering if there was a general for formula to calculate the combination of the password lock for the current smart phones

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The following is the condition

  1. We must use four nodes or more to make a pattern at least.
  2. Once anode is visited, then the node can't be visited anymore.
  3. You can start at any node.
  4. A pattern has to be connected.
  5. Cycle is not allowed.

If using 4 as the minimum string for the password with 9 nodes , the result is 389112.

Is there anyway to estimate the number of combinations for 16 nodes, 25 nodes and so on?