I agree on staying with tested solutions. However, I just wanted to leave an idea on how it can be done by using a starting date (I chose the first Sunday of this year). You wouldn't need the CTE, it's just there to simulate the different weeks.

WITH

E(n) AS(

SELECT n FROM (VALUES(0),(0),(0),(0),(0),(0),(0),(0),(0),(0))E(n)

),

E2(n) AS(

SELECT a.n FROM E a, E b

),

E4(n) AS(

SELECT a.n FROM E2 a, E2 b

),

cteTally(n) AS(

SELECT TOP 52 ROW_NUMBER() OVER(ORDER BY (SELECT NULL)) - 1 n

FROM E4

),

Weeks(GetSunday) AS(

SELECT DATEADD( WK, n, '20160102')

FROM cteTally

)

SELECT 'BACKUP DATABASE AdventureWorks2012 TO DISK = ''Z:\SQLServerBackups\'

+ CASE WHEN DATEDIFF( WK, '20160102', GetSunday) % 3 = 0 THEN 'AdvWorksData1'

WHEN DATEDIFF( WK, '20160102', GetSunday) % 3 = 1 THEN 'AdvWorksData2'

WHEN DATEDIFF( WK, '20160102', GetSunday) % 3 = 2 THEN 'AdvWorksData3'

END

+ '.bak'' WITH FORMAT;',

GetSunday

FROM Weeks