The sequence of pizza numbers (Pn)n≥o (the maximal number of pieces formed when slicing a pizza with n cuts) starts 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56. ... Note, in here we think of a pizza as a flat 2-dimensional disc. (a) Draw two pictures to show P3 = 7, and P4 = = 11. (b) Compute the sequence of first differences. (c) Compute the sequence of second differences. (d) Use polynomial fitting to find the closed formula for the sequence Pn.

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