fibonacci_cte.sql

WITH RECURSIVE fibonacci(recursion_level, fibonacci_number, next_number)
 AS (
# Base Case
SELECT  0 AS recursion_level,
        0 AS fibonacci_number,
        1 AS next_number
UNION ALL
# Recursion query
SELECT  recursion_level + 1             AS recursion_level,
        next_number                     AS fibonacci_number,
        fibonacci_number + next_number  AS next_number
FROM fibonacci
WHERE
  recursion_level < 10
)

SELECT * FROM fibonacci

fibonacci_cte_postgres.sql

  WITH RECURSIVE fibonacci(fibonacci_number, next_number)
   AS (

  SELECT
          0 AS fibonacci_number,
          1 AS next_number
  UNION ALL

  SELECT
          next_number                     AS fibonacci_number,
          fibonacci_number + next_number  AS next_number
  FROM fibonacci
  )

  SELECT * FROM fibonacci
LIMIT 10;

+-----------------+------------------+-------------+
| recursion_level | fibonacci_number | next_number |
+-----------------+------------------+-------------+
|               0 |                0 |           1 |
|               1 |                1 |           1 |
|               2 |                1 |           2 |
|               3 |                2 |           3 |
|               4 |                3 |           5 |
|               5 |                5 |           8 |
|               6 |                8 |          13 |
|               7 |               13 |          21 |
|               8 |               21 |          34 |
|               9 |               34 |          55 |
|              10 |               55 |          89 |
+-----------------+------------------+-------------+