What is the pattern in the sequence 1, 1, 0, -1, 0, 7, 28, 79, 192?

1 Answer
Jul 31, 2015

#a_n = 2^n-n^2# for #n=0, 1, 2,...#

Explanation:

Start with the sequence:
#1, 1, 0, -1, 0, 7, 28, 79, 192#

Form the sequence of differences:
#0, -1, -1, 1, 7, 21, 52, 113#

Then the sequence of differences of those differences:
#-1, 0, 2, 6, 14, 30, 62#

Then the sequence of differences of those differences:
#1, 2, 4, 8, 16, 32#

Subtract this from the original sequence to get:
#0, -1, -4, -9, -16, -25#

This is obviously a sequence of negated square numbers.

So #a_n = 2^n-n^2#