- #1

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## Main Question or Discussion Point

If we have a positive integer, how many ways can this number be written as a sum of its components? By components, I mean all numbers less than that number.

For example, 5 has 6 ways to be written;

5x1, 3x1+2, 2x2+1, 2x1+3,1+4 and 2+3. In digits form; [11111, 1112, 221,113, 14, 23]

So there are 6 ways to write 5.

For number 6; [111111, 11112,1113,114,15, 2+4, 3+3, 1+2+3, 2+2+2 and 1+2+2+1]. which is 10.

In general how many ways to write a number as a sum of all possible combination of numbers less than that number?

For example, 5 has 6 ways to be written;

5x1, 3x1+2, 2x2+1, 2x1+3,1+4 and 2+3. In digits form; [11111, 1112, 221,113, 14, 23]

So there are 6 ways to write 5.

For number 6; [111111, 11112,1113,114,15, 2+4, 3+3, 1+2+3, 2+2+2 and 1+2+2+1]. which is 10.

In general how many ways to write a number as a sum of all possible combination of numbers less than that number?