母牛的问题怎么算？

来源：百度知道 编辑：UC知道 时间：2024/04/28 11:53:26
我有一道数学题：有一头母牛，它每年年初生一头小母牛。每头小母牛从第四个年头开始，每年年初也生一头小母牛。请问第n年时共有多少头母牛？
能讲解一下思考过程吗？多谢！O(∩_∩)O

f[0] = 1; f[1] = 2; f[2] = 3;
f[x_] := f[x - 1] + f[x - 3]
程序解得:
{年,牛数}
{0, 1},
{1, 2},
{2, 3},
{3, 4},
{4, 6},
{5, 9},
{6, 13},
{7, 19},
{8, 28},
{9, 41},
{10, 60},
{11, 88},
{12, 129},
{13, 189},
{14, 277},
{15, 406},
{16, 595},
{17, 872},
{18, 1278},
{19, 1873},
{20, 2745},
{21, 4023},
{22, 5896},
{23, 8641},
{24, 12664},
{25, 18560},
{26, 27201},
{27, 39865},
{28, 58425},
{29, 85626},
{30, 125491},
{31, 183916},
{32, 269542},
{33, 395033},
{34, 578949},
{35, 848491},
{36, 1243524},
{37, 1822473},
{38, 2670964},
{39, 3914488},
{40, 5736961},
{41, 8407925},
{42, 12322413},
{43, 18059374}

不好意思,离散数学我没学过.

1+1+1+1+1+2+3+4+5+7+10+14+19+26+36+50+69+95+131+180+...

我只能这么推算了