YLL討論網

#ed_op#DIV#ed_cl#是的#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#Fibonacci sequence 的定義即為#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#F0=0   F1=1   F(n+2)=F(n+1)+F(n)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以為 0,1,1,2,3,5,8,13,21,34,55,89...#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#而一般通式大概就是大家知道的#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#Fn=1/√5[(1+√5 /2)^n - (1-√5 /2)^n]#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#我覺得這就很漂亮了啊 ^^#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#如果你利用 golden ratio 代入的話是可以得到比較"好看"一點的式子 #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#不過基本上視情況來看要用哪種式子會比較好#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#Fabonacci sequence 在大學Number Theory裡都只有一小篇章,資料有限#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#不過MathWorld有不少資料,可以查查看,相信對你會有幫助的#ed_op#/DIV#ed_cl#

#ed_op#DIV#ed_cl#請問是不是從(0,1)開始的才叫Fibonacci number?#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#其他的如(1,4)開始的 => 1 4 5 9 14 23 ......等等...... 也算是嗎?#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#還有，Fibonacci number有沒有比 Fc(n+2)=Fc(n)+Fc(n+1) 更簡單的公式呢?#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#聽說 round( [(1+√5)/2]#ed_op#SUP#ed_cl#n #ed_op#/SUP#ed_cl#/ √5 ) 可以得出結果，是真的嗎?#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#謝謝回答！#ed_op#/DIV#ed_cl#