Question: 2.1. DESCRIBING SEQUENCES 147 explain a recurrence relation for the sequence (an) which gives the number of strings with sum n. (d) Describe what you

2.1. DESCRIBING SEQUENCES 147 explain a recurrence relation for the sequence (an) which gives the number of strings with sum n. (d) Describe what you have found above in terms of Pascal's Trian- gle. What pattern have you discovered? 18. When bees play chess, they use a hexagonal board like the one shown below. The queen bee can move one space at a time either directly to the right or angled up-right or down-right (but can never move leftwards). How many different paths can the queen take from the top left hexagon to the bottom right hexagon? Explain your answer, and this relates to the previous question. (As an example, there are three paths to get to the second hexagon on the bottom row.) start 3 stop 19

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