Hello all,(adsbygoogle = window.adsbygoogle || []).push({});

I have been thinking about a particular mathematical question (that I've made up) and I haven't been able to reach a solution yet..

I want to find the rule for the function F(x,y) which gives the number of different "ways" that the integer x can be expressed as the summation of "y" pieces of integers (these integers have to be bigger than or equal to 1) (sorry for my awful technical English

Let me clarify it with an example:

When we consider F(9,4), it can be observed that

9 = 1+1+1+6

9 = 1+1+2+5

9 = 1+1+3+4

9 = 1+2+2+4

9 = 1+2+3+3

9 = 2+2+2+3

Following from here, since there are 6 different ways of expressing this summation,

F(9,4)=6

In the above example, (1+1+1+6) and, for example, (1+6+1+1) are considered to be the same and thus are counted only once.

NOTE: When we consider (1+1+1+6) and (1+6+1+1) to be different ways of summation, for instance, the problem becomes very easy and can be solved by pigeon hole principle. But the tricky part for me is to find a formula which considers the two expressions above and such to amount to the same.

Thanks!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The number of ways to express a specific summation

Loading...

Similar Threads for number ways express | Date |
---|---|

Number of ways to select M cohyperplanar points in finite space | Jul 28, 2014 |

Number of unique ways of stacking n blocks | Jan 9, 2013 |

Is there any way to find the product of prime numbers? | Sep 4, 2011 |

Number of ways to choose N integers that sum up to X | May 6, 2011 |

Writing numbers in statistical way? | Apr 8, 2011 |

**Physics Forums - The Fusion of Science and Community**