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Increasing the number of circles

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Reference no: EM131985714

If you have ever tried making patterns with a collection of coins, you have probably noticed that you can make hexagons in a natural way by packing circles as tightly as possible. The figure below shows how 19 circles fit into a hexagonal shape with 3 circles on each edge. Let H(n) be the number of circles you need to form a hexagon with n circles on each edge. From the figure below, it is clear that H(2) = 7 and H(3) = 19.

It can be shown that increasing the number of circles on each edge gives the following recurrence relation:

H(n) = 1  if n = 1H(n - 1) + 6n - 6  if n > 1.

Calculate H(6).

Reference no: EM131985714

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