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Any sequence including n + 1 is a new sequence. For the mapping we can think about it like this : Total = New + Old Old = An-1 where n is effectively n + 1 I am not exactly sure on how to compute the number of new possible combinations

Homework Statement Find a recurrence relation for the number of stricly increasing sequences of positive integers that have 1 as their first term and n as their last term, where n is a positive integer. that is, sequences a1, a2, ..., ak, where a1 = 1, ak = n, and aj < aj+1 for j = 1, 2...

Ah it makes sense now. Thanks a lot Sunil, you have helped me greatly.

Then they must be both even. But my question is, how can I proof that the parity must be even. I just said it because I did a few examples and it made sense. But how do you actually know it must be even?

Well the parity must be even for a tour to be able to be completed.

How do I calculate parity?

0, 2, 4, 6, ... (all the even number of steps) have the same color and all the odds have the same color.

The colors change. From black to white.

Since a tour is all squares, then it is pq.

Homework Statement Consider a grid with height p >= 2 and width q >= 2, so there are pq squares in the grid. A valid walk on the grid is a walk that starts on one square and subsequently moves to adjacent squares (you cannot move diagonally). Define a tour to be a valid walk on the grid that...