Saturday, 16 April 2016

Find the nth term for this sequence



I have the following sequence:




4, 7, 11, 19, 36, 69





Now, I've done the usual and found the differences, and it goes down to four levels until I get a common difference, suggesting I have to use n4 somewhere, but I just can't find the nth term. Any help? And if you know of any easier methods to finding the nth term, I'd appreciate it.



P.S. - I know about the formulas for arithmetic progression and geometric progression, but clearly neither can be used here.


Answer



The first numbers in each row of differences are 4, 3, 1, 3, 2. Assuming that the last row is all 2's then the formula is
4(n0)+3(n1)+1(n2)+3(n3)+2(n4)

starting at n=0.
This is an instance of the Newton series.



The formula simplifies to
n4n2+36n+4812
but this is not enlightening.


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