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I've been trying to find out the ways in which an odd integral number can be represented by smaller integers such that the even integers occur an even number of times. So for example, the number 15 has the following representations:

15: 2+2+2+2+2+2+3 (even integer 2 occurs even number of times i.e. 6 times)

15: 4+2+2+2+5 (even integers 4 and 2 combined occur 4 times - 2 occurs thrice and 4 occurs once)

15: 6+2+2+2+3 and so on.

I've been trying to derive an analytical formula for this problem. Any ideas anyone?

Thanks

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# Related to partition theory, ways of representing a number

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