The Vedic Mathematics Sutras
This list of sutras is taken from the book Vedic Mathematics, which includes a full list of the sixteen Sutras in Sanskrit, but in some cases a translation of the Sanskrit is not given in the text and comes from elsewhere.
This formula 'On the Flag' is not in the list given in Vedic Mathematics, but is referred to in the text.
The Sixteen Sutras
Sutra  Translation  
1  By one more than the one before  
2  All from 9 and the last from 10  
3  Vertically and Crosswise  
4  Transpose and Apply  
5  If the Samuccaya is the Same it is Zero  
6  If One is in Ratio the Other is Zero  
7 

By Addition and by Subtraction 
8 

By the Completion or NonCompletion 
9  Differential Calculus  
10  By the Deficiency  
11  Specific and General  
12  The Remainders by the Last Digit  
13  The Ultimate and Twice the Penultimate  
14  By One Less than the One Before  
15  The Product of the Sum  
16  All the Multipliers 
Note: The current Shankaracharya of Puri, Jagadguru Swami Nishchalananda Saraswati, has said (in 2008) he will be able to locate all the above sutras in the Vedic texts, but has so far only found one.
See also the article "The Sutras of Vedic Mathematics", by Kenneth Williams, published in the Journal of the Oriental Institute.
The Sub Sutras
Sub Sutra  Translation  
1  Proportionately  
2  The Remainder Remains Constant  
3  The First by the First and the Last by the Last  
4  For 7 the Multiplicand is 143  
5  By Osculation  
6  Lessen by the Deficiency  
7  Whatever the Deficiency lessen by that amount and set up the Square of the Deficiency  
8  Last Totalling 10  
9  Only the Last Terms  
10  The Sum of the Products  
11  By Alternate Elimination and Retention  
12  By Mere Observation  
13  The Product of the Sum is the Sum of the Products  
14  On the Flag 