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what is a recursive formula that represents the pentagonal numbers. 1 8 21 40 65 96 133 176 225 280 341 408 481 560 645 736 833 936 sequence A000567 in the OEIS. For example suppose we know the following.
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We then incorporated the formula for a -gon which in the case of the pentagonal fractal is a decagon. What is the nth pentagonal number in terms of triangular numbers. S_n represents the nth number in the sequence and its formula is n² which can be directly computed by plugging in the value of n you want.
The first few octagonal numbers are.
For a sequence a 1 a 2 a 3. A recursive formula is a formula that requires the computation of all previous terms in order to find the value of a n. By examining the array in Figure 5 one can come up with the following recursive formulas where P n represents the n-th pentagonal numberP 1 1P 2 P 1 4P 3 P 2 7P 4 P 3 10One can guess the formula for P nP n P n-1 3n - 2 and this is correct. A n.
