I think Fib(182) is as far as one can go with SQL Server.
I used the answer from @Pavel Pawlowski to create a Fib-function to test it.
CREATE FUNCTION dbo.Fib(@n int)
RETURNS numeric(38,0)
AS
BEGIN
DECLARE @i numeric(38,0);
WITH Fib(Num, fib, fib2) AS (
SELECT 0 AS Expr1, cast(0 as numeric(38,0)) AS Expr2, cast(1 as numeric(38,0)) AS Expr3
UNION ALL
SELECT Num + 1 AS Expr1, fib + fib2 AS Expr2, fib
FROM Fib AS fib_2
WHERE (Num
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