这个网站是由捐款支持的OEIS基金会.

N-bonacci数

来自OeisWiki
跳转到:航行,搜索


这篇文章的页面是一个存根,请扩展一下。


这个N-bonacci数源于递推关系就像那个斐波纳契数,但是初始术语定义为

而不是两个初始项,并且每个后续项都是前一项的总和条款

最常见的选择第一个项的初始项要么都是0,要么都是1初始条款,,1代表第个初始期限.

第一个N-1初始项设置为0,第N个初始项设置为1的N-bonacci数

这个N-bonacci数初始条件设置为. 以后的每一项都是前一项的总和条款。例如,47个bonacci数使用一个递归关系,其中46个初始值为0,1个为1,随后的每个项都是前47个项的总和。

-博纳契数
-博纳契数列 A-编号
0 {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,…} A000004号
1 {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,…] A000012号
2 {0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,…] A000045型
{0,0,1,1,2,4,7,13,24,44,81,149,274,504,927,1705,3136,5768,10609,19513,35890,66012,121415,223317,410744,755476,1389537,2555757,4700770,8646064,…} A000073号
4 {0,0,0,1,1,2,4,8,15,29,56,108,208,401,773,1490,2872,5536,10671,20569,39648,76424,147312,283953,547337,1055026,2033628,3919944,7555935,14564533,…} A000078号
5 {0,0,0,0,1,1,2,4,8,16,31,61,120,236,464,912,1793,3525,6930,13624,26784,52656,103519,203513,400096,786568,1546352,3040048,5976577,11749641,…} A001591号
6 {0,0,0,0,1,1,2,4,8,16,32,63,125,248,492,976,1936,3840,7617,15109,29970,59448,117920,233904,463968,920319,1825529,3621088,718272814247536,…} A001592号
7 {0,0,0,0,0,1,1,2,4,8,16,32,64,127,253,504,1004,2000,3984,7936,15808,31489,62725,124946,24888,495776,987568,1967200,3918592,7805695,…] A122189号
8 {0,0,0,0,0,0,1,1,2,4,8,16,32,64,128,255,509,1016,2028,4048,8080,16128,32192,64256,128257,256005,510994,1019960,2035872,4063664,8111200,…} A079262号
9 {0,0,0,0,0,0,0,1,1,2,4,8,16,32,64,128,256,511,1021,2040,4076,8144,16272,32512,64960,129792,259328,518145,1035269,2068498,4132920,8257696,…] A104144号
10 {0,0,0,0,0,0,0,0,1,1,2,4,8,16,32,64,128,256,512,1023,2045,4088,8172,16336,32656,65280,130496,260864,521472,1042432,2083841,4165637,8327186,…} 邮编:A122265
11 {}  
12 {}  

所有N个初始项都设置为1的N-bonacci数

  1.  
  2.  
  3. A000213tribonaci数:a(n)=a(n-1)+a(n-2)+a(n-3),其中a(0)=a(1)=a(2)=1。
  4. A000288号Tetranacci数:a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4),其中a(0)=a(1)=a(2)=a(3)=1。
  5. A000322号Pentanacci数:a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5),其中a(0)=a(1)=a(2)=a(3)=a(4)=1。
  6.  
  7.  
  8.  
  9. A127193号一个9阶Fibonacci序列,A(1)=…=A(9)=1。
  10. A127194号一个10阶Fibonacci序列,A(1)=…=A(10)=1。
  11. 邮编:A12762411阶Fibonacci序列。a(n)=a(n-1)+。。。+a(n-11),其中a(1)=…=a(11)=1。
  12. A207539号Dodecanacci数(12阶Fibonacci序列):a(n)=a(n-1)+…+a(n-12),其中a(0)=…=a(11)=1。
  13. 邮编:A16355113阶Fibonacci数:a(n)=a(n-1)+…+a(n-13),其中a(1)=…=a(13)=1。

N个初始项设置为其他值的N-bonacci数

  • A001630型Tetranacci数:a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4),其中a(0)=a(1)=0,a(2)=1,a(3)=2。

另请参见

笔记