"소모스 수열(Somos sequence)"의 두 판 사이의 차이

2011년 2월 24일 (목) 13:03 판

t_n+5 = (t_n+4 t_n+1 + t_n+3 t_n+2)/t_n
with initial values (1,1,1,1,1).

\(t_{n+5} = (t_{n+4} t_{n+1} + t_{n+3} t_{n+2})/t_{n}\)

\(a_{n+4}a_{n} = a_{n+3} a_{n+2} + a_{n+1}^2\)
1, 1, 1, 1, 2, 3, 7, 23, 59, 314, 1529, 8209, 83313, 620297, 7869898, 126742987, 1687054711, 47301104551, 1123424582771, 32606721084786

RecurrenceTable[{a[n] a[n - 4] == a[n - 1] a[n - 3] + a[n - 2]^2,
a[1] == 1, a[2] == 1, a[3] == 1, a[4] == 1}, a, {n, 10}]

\(a_{n+5}a_{n} = a_{n+4} a_{n+1} + a_{n+3} a_{n+2}\)
1, 1, 1, 1, 1, 2, 3, 5, 11, 37, 83, 274, 1217, 6161, 22833, 165713, 1249441, 9434290, 68570323, 1013908933

RecurrenceTable[{a[n] a[5 + n] ==
a[2 + n] a[3 + n] + a[1 + n] a[4 + n], a[1] == 1, a[2] == 1,
a[3] == 1, a[4] == 1, a[5] == 1}, a, {n, 20}]

@@ 17번째 줄: / 17번째 줄: @@
 <h5 style="margin: 0px; line-height: 2em;">소모스 4-수열</h5>
-#  RecurrenceTable[{a[n] a[n - 4] == a[n - 1] a[n - 3] + a[n - 2]^2,<br>   a[1] == x, a[2] == b, a[3] == c, a[4] == d}, a,<br>    {n, 10}]<br>
+* <math>a_{n+4}a_{n} = a_{n+3} a_{n+2} + a_{n+1}^2</math><br>
+*  1, 1, 1, 1, 2, 3, 7, 23, 59, 314, 1529, 8209, 83313, 620297, 7869898, 126742987, 1687054711, 47301104551, 1123424582771, 32606721084786<br>
+#  RecurrenceTable[{a[n] a[n - 4] == a[n - 1] a[n - 3] + a[n - 2]^2,<br>  a[1] == 1, a[2] == 1,   a[3] == 1, a[4] == 1}, a,    {n, 10}]<br>
+<h5 style="margin: 0px; line-height: 2em;">소모스 5-수열</h5>
+* <math>a_{n+5}a_{n} = a_{n+4} a_{n+1} + a_{n+3} a_{n+2}</math><br>
+*  1, 1, 1, 1, 1, 2, 3, 5, 11, 37, 83, 274, 1217, 6161, 22833, 165713, 1249441, 9434290, 68570323, 1013908933<br>
+#  RecurrenceTable[{a[n] a[5 + n] ==<br>    a[2 + n] a[3 + n] + a[1 + n] a[4 + n], a[1] == 1, a[2] == 1,<br>   a[3] == 1, a[4] == 1, a[5] == 1}, a,   {n, 20}]<br>