How to calculate conditional running additions in SQL Server 2012

Question

I have a table with below mentioned structure

create table #test
(
ID int identity(1,1),
A int,
B int
);

and having data as

ID A B
1 9 NULL
2 9 1
3 9 2
4 8 NULL
5 8 4
6 8 5

I want to calculate a new column let us say C based on values of this table. If we consider it as an excel table then, formula for calculation would be =IF(B1="",C1+A2,B1+A2). i.e. first value of calculated column would always be A1 and then from second row I have to apply above excel formula in SQL SERVER 2012 to calculate a new column.

I am aware about LAG and LEAD functions, but my computation involves value of computed column of previous row for computation of current computing value.

I am clueless about such calculation in SQL SERVER. What would be the best way to compute such a condition?

EDIT Expected output would be

9
18
10
10
18
12

The select statement which I tried is

SELECT
 CASE WHEN LAG(B) OVER (order by ID) is null THEN 351
 ELSE LAG(B)
 OVER (order by ID) + A END
FROM #test;

EDIT 2 Test Data:

INSERT INTO #test (A, B)
VALUES 
 (NULL,355)
 ,(NULL,NULL)
 ,(NULL,NULL)
 ,(NULL,NULL)
 ,(NULL,NULL)
 ,(NULL,NULL)

Result:

0
355
355
355
355
355

Answer 1

Below is a CTE method to facilitate evaluating values from the previous row with LAG.

CREATE TABLE #test
(
 ID int IDENTITY
 , A int
 , B int
);
INSERT INTO #test (A, B)
VALUES
 (9, NULL)
 , (9, 1)
 , (9, 2)
 , (8, NULL)
 , (8, 4)
 , (8, 5);
WITH test AS (
 SELECT
 ID
 , A
 , LAG(A) OVER(ORDER BY ID) AS prev_A
 , LAG(B) OVER(ORDER BY ID) AS prev_B
 , A + COALESCE(LAG(B) OVER(ORDER BY ID), 0) AS C
 FROM #test
)
SELECT
 A + COALESCE(CASE 
 WHEN prev_B IS NOT NULL THEN prev_B
 ELSE LAG(C) OVER(ORDER BY ID)
 END, 0) AS C
FROM test
ORDER BY ID;

EDIT

To handle the NULL A values in the edited question, try the recursive CTE method below.

WITH
 curr AS (
 SELECT
 A
 , B
 , ROW_NUMBER() OVER (ORDER BY ID) AS rownum
 FROM #test
 )
 , prev AS (
 SELECT
 A
 , B
 , COALESCE(A, 0) AS C
 , rownum
 FROM curr
 WHERE rownum = 1
 UNION ALL
 SELECT
 curr.A
 , curr.B
 , CASE
 WHEN prev.B IS NULL THEN prev.C + COALESCE(curr.A, 0)
 ELSE prev.B + COALESCE(curr.A, 0)
 END AS C
 , curr.rownum
 FROM prev
 JOIN curr ON curr.rownum = prev.rownum + 1
 )
SELECT C
FROM prev;