dynamic_programming.py

def count_sequences(start_position, num_hops):                
    prior_case = [1] * 10                                     
    current_case = [0] * 10                                   
    current_num_hops = 1                                      
                                                              
    while current_num_hops <= num_hops:                       
        current_case = [0] * 10                               
        current_num_hops += 1                                 
                                                              
        for position in range(0, 10):                         
            for neighbor in neighbors(position):              
                current_case[position] += prior_case[neighbor]
        prior_case = current_case                             
                                                              
    return current_case[start_position]                       

Transcribed to Javascript for those interested

class KnightsDialer {
  constructor() {
      this.NEIGHBORS_MAP = {
        1: [6, 8],
        2: [7, 9],
        3: [4, 8],
        4: [3, 9, 0],
        5: [],
        6: [1, 7, 0],
        7: [2, 6],
        8: [1, 3],
        9: [2, 4],
        0: [4, 6]
    };
  }

  countSequences(startPosition, numHops) {
    let priorCase = Array(10).fill(1);
    let currentCase = Array(10).fill(0);
    currentNumHops = 1;

    while (currentNumHops <= numHops) {
      currentCase = Array(10).fill(0);
      currentNumHops += 1;

      for (let position = 0; position < 10; position++) {
        for (const neighbor of this.NEIGHBORS_MAP[position]) {
          currentCase[position] += priorCase[neighbor];
        }
      }
      priorCase = currentCase;
    }
    return currentCase[startPosition];
  }
}

const kd = new KnightsDialer();
console.log(kd.countSequences(6,2)); // output: 6