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...
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?
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...