0
             1
             1
             2
             3
             5
             8
            13
            21
            34
            55
            89

SQL> DEFINE N=12
SQL> SELECT ' F('||num||') = '||fibo "Fibonacci" 
  2  FROM ( SELECT 1 rn FROM DUAL )
  3  MODEL
  4    DIMENSION BY (rn)
  5    MEASURES (0 num, 1 fibo)
  6    RULES
  7      ITERATE (&N)
  8      ( num[ITERATION_NUMBER] = ITERATION_NUMBER,
  9        fibo[ITERATION_NUMBER] = 
 10          CASE 
 11          WHEN ITERATION_NUMBER IN (0,1) THEN ITERATION_NUMBER
 12          ELSE fibo[CV()-1] + fibo[CV()-2] 
 13          END
 14      )
 15  ORDER BY num
 16  /
Fibonacci
------------------------------------------------------------------
 F(0) = 0
 F(1) = 1
 F(2) = 1
 F(3) = 2
 F(4) = 3
 F(5) = 5
 F(6) = 8
 F(7) = 13
 F(8) = 21
 F(9) = 34
 F(10) = 55
 F(11) = 89

12 rows selected.

SQL> SELECT ' F('||rn||') = '||fibo "Fibonacci" 
  2  FROM ( SELECT rownum-1 rn FROM DUAL CONNECT BY LEVEL <= &N )
  3  MODEL
  4    DIMENSION BY (rn)
  5    MEASURES (1 fibo)
  6    RULES 
  7      ( fibo[ANY] = 
  8          CASE 
  9          WHEN CV(rn) IN (0,1) THEN CV(rn)
 10          ELSE fibo[CV()-1] + fibo[CV()-2] 
 11          END 
 12      )
 13  ORDER BY rn
 14  /
Fibonacci
------------------------------------------------------------------
 F(0) = 0
 F(1) = 1
 F(2) = 1
 F(3) = 2
 F(4) = 3
 F(5) = 5
 F(6) = 8
 F(7) = 13
 F(8) = 21
 F(9) = 34
 F(10) = 55
 F(11) = 89

12 rows selected.

SQL> select level - 1 "LEVEL"
  2     , (1 / sqrt(5)) *
  3     (power(((1 + sqrt(5))/2), level - 1) - power(((1 - sqrt(5))/2), level - 1)) fibonacci
  4  from dual
  5  connect by level < 13;

     LEVEL  FIBONACCI
---------- ----------
         0          0
         1          1
         2          1
         3          2
         4          3
         5          5
         6          8
         7         13
         8         21
         9         34
        10         55
        11         89

12 rows selected.

SQL> CREATE OR REPLACE TYPE FIBONACCI as table OF NUMBER(10);
  2  /

Type created.

SQL> CREATE OR REPLACE FUNCTION gen_fibonacci (series_length IN NUMBER)
  2  RETURN FIBONACCI PIPELINED
  3  AS
  4  n0 NUMBER :=0;
  5  n1 NUMBER :=1;
  6  n2 NUMBER :=0;
  7  BEGIN
  8      PIPE ROW(n0);
  9      PIPE ROW(n1);
 10    FOR i IN n0..series_length-3
 11    LOOP
 12      n2 := n0 + n1 ;
 13      PIPE ROW(n2);
 14      n0 := n1;
 15      n1 := n2;
 16    END LOOP;
 17    RETURN;
 18  END gen_fibonacci;
 19  /

Function created.

SQL> select COLUMN_VALUE FIBONACCI
  2  from TABLE(gen_fibonacci(10));

 FIBONACCI
----------
         0
         1
         1
         2
         3
         5
         8
        13
        21
        34

10 rows selected.

SQL>

SCOTT@orcl_11gR2> with
  2    numbers (lvl, fibonacci, next) as
  3  	 (select 0, 0, 1
  4  	  from	 dual
  5  	  union  all
  6  	  select lvl + 1, next, fibonacci + next
  7  	  from	 numbers
  8  	  where  lvl <= 10)
  9  select lvl "LEVEL", fibonacci
 10  from   numbers
 11  order  by lvl
 12  /

     LEVEL  FIBONACCI
---------- ----------
         0          0
         1          1
         2          1
         3          2
         4          3
         5          5
         6          8
         7         13
         8         21
         9         34
        10         55
        11         89

12 rows selected.