SQL Server 2019

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/*  DATA SETUP  */
CREATE TABLE #Table (SortID int IDENTITY(1,1), BitValue bit);
INSERT INTO #Table (BitValue)
VALUES (0), (1), (1), (1), (0), (1), (1);

SELECT * FROM #Table;



SortID
BitValue


1
False

2
True

3
True

4
True

5
False

6
True

7
True


/*  ANSWER  */

DECLARE @a int;
SET @a = 2;

WITH Grouped_BitValues AS
    (SELECT SortID, BitValue, 
            CASE WHEN BitValue = 0 THEN 1 ELSE 0 END AS NewGrpFlag,
            SUM(CASE WHEN BitValue = 0 THEN 1 ELSE 0 END) OVER (ORDER BY SortID) AS GroupNum            
    FROM    #Table
    )
SELECT  BitValue, POWER(@a, ROW_NUMBER() OVER (PARTITION BY GroupNum ORDER BY SortID) -1) AS Geometric_Sequence
FROM Grouped_BitValues
ORDER BY SortID;



BitValue
Geometric_Sequence


False
1

True
2

True
4

True
8

False
1

True
2

True
4


/*  CTE Component  */

SELECT  SortID, BitValue, 
        CASE WHEN BitValue = 0 THEN 1 ELSE 0 END AS NewGrpFlag,
        SUM(CASE WHEN BitValue = 0 THEN 1 ELSE 0 END) OVER (ORDER BY SortID) AS GroupNum
FROM    #Table;



SortID
BitValue
NewGrpFlag
GroupNum


1
False
1
1

2
True
0
1

3
True
0
1

4
True
0
1

5
False
1
2

6
True
0
2

7
True
0
2


/*  ALL DATA (WITH @a = 2)  */

WITH Grouped_BitValues AS
    (SELECT SortID, BitValue, 
            CASE WHEN BitValue = 0 THEN 1 ELSE 0 END AS NewGrpFlag,
            SUM(CASE WHEN BitValue = 0 THEN 1 ELSE 0 END) OVER (ORDER BY SortID) AS GroupNum            
    FROM    #Table
    )
SELECT  Grouped_BitValues.*, POWER(2, ROW_NUMBER() OVER (PARTITION BY GroupNum ORDER BY SortID) -1) AS Geometric_Sequence
FROM Grouped_BitValues
ORDER BY SortID;



SortID
BitValue
NewGrpFlag
GroupNum
Geometric_Sequence


1
False
1
1
1

2
True
0
1
2

3
True
0
1
4

4
True
0
1
8

5
False
1
2
1

6
True
0
2
2

7
True
0
2
4