Xiaohu trains to run up the stairs. He can go up 1 step, 2 steps or 3 steps with each step. In this way, he goes up to 16 steps but does not step on the 7th and 15th steps. How many different ways are there?
小虎训练上楼梯赛跑，他每步可上1阶或2阶或3阶，这样上到16阶但不踏到第7阶和第15阶，那么不同的上法共有多少种？
<gadget id="calculator">2 + 4 + 7</gadget>
<output>13</output>

<gadget id="calculator">4 + 7 + 13</gadget>
<output>24</output>

<gadget id="calculator">13 + 24</gadget>
<output>37</output>

<gadget id="calculator">37 + 61</gadget>
<output>98</output>

<gadget id="calculator">37 + 61 + 98</gadget>
<output>196</output>

<gadget id="calculator">61 + 98 + 196</gadget>
<output>355</output>

<gadget id="calculator">98 + 196 + 355</gadget>
<output>649</output>

<gadget id="calculator">196 + 355 + 649</gadget>
<output>1_200</output>

<gadget id="calculator">649 + 1_200</gadget>
<output>1_849</output>

<result>1_849</result>