Data commit

Task/Fibonacci-sequence/SQL/fibonacci-sequence-1.sql

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+select round ( exp ( sum (ln ( ( 1 + sqrt( 5 ) ) / 2)
+        ) over ( order by level ) ) / sqrt( 5 ) ) fibo
+from dual
+connect by level <= 10;

Task/Fibonacci-sequence/SQL/fibonacci-sequence-2.sql

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+select round ( power( ( 1 + sqrt( 5 ) ) / 2, level ) / sqrt( 5 ) ) fib
+from dual
+connect by level <= 10;

Task/Fibonacci-sequence/SQL/fibonacci-sequence-3.sql

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+SQL> with fib(e,f) as (select 1, 1 from dual union all select e+f,e from fib where e <= 55) select f from fib;
+
+         F
+----------
+         1
+         1
+         2
+         3
+         5
+         8
+        13
+        21
+        34
+        55
+
+10 rows selected.

Task/Fibonacci-sequence/SQL/fibonacci-sequence-4.sql

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+CREATE FUNCTION fib(n int) RETURNS numeric AS $$
+    -- This recursive with generates endless list of Fibonacci numbers.
+    WITH RECURSIVE fibonacci(current, previous) AS (
+        -- Initialize the current with 0, so the first value will be 0.
+        -- The previous value is set to 1, because its only goal is not
+        -- special casing the zero case, and providing 1 as the second
+        -- number in the sequence.
+        --
+        -- The numbers end with dots to make them numeric type in
+        -- Postgres. Numeric type has almost arbitrary precision
+        -- (technically just 131,072 digits, but that's good enough for
+        -- most purposes, including calculating huge Fibonacci numbers)
+        SELECT 0., 1.
+    UNION ALL
+        -- To generate Fibonacci number, we need to add together two
+        -- previous Fibonacci numbers. Current number is saved in order
+        -- to be accessed in the next iteration of recursive function.
+        SELECT previous + current, current FROM fibonacci
+    )
+    -- The user is only interested in current number, not previous.
+    SELECT current FROM fibonacci
+    -- We only need one number, so limit to 1
+    LIMIT 1
+    -- Offset the query by the requested argument to get the correct
+    -- position in the list.
+    OFFSET n
+$$ LANGUAGE SQL RETURNS NULL ON NULL INPUT IMMUTABLE;