Question: General Form of Sequence
Sunday, 24 of February , 2008 at 12:34 pm
Question: The solution to 
where 
yields the following sequence:
8, 12, 36, 44, 84, 96, 152, 168, 240…
Find the general form for this sequence.
Question: The solution to where yields the following sequence:
Find the general form for this sequence.
Comment by eldila
Made Sunday, 24 of February , 2008 at 12:37 pm
The sequence can be expanded to give the following terms:
8, 12, 36, 44, 84, 96, 152, 168, 240, 260, 348, 372, 476, 504, 624, 656, 792, 828, 980, 1020, 1188, 1232, 1416, 1464, 1664, 1716, 1932, 1988, 2220, 2280, 2528, 2592, 2856, 2924, 3204, 3276, 3572, 3648, 3960, 4040, 4368, 4452, 4796, 4884, 5244, 5336, 5712, 5808, 6200, 6300, 6708, 6812, 7236, 7344, 7784, 7896, 8352, 8468, 8940, 9060, 9548, 9672 …
Comment by Vishal
Made Tuesday, 26 of February , 2008 at 8:30 am
One way would be to note that all the terms are divisible by 4. So, if we factor 4 out, then the terms will be 2, 3, 9, 11, 21, 24, 38, 42,…
Now, if we group those terms in pairs, then we obtain (2,3), (9,11), (21,24), (38,42), …
Now, one can easily see that the difference between the numbers in each pair is 1, 2, 3, 4 and so on. Also, 9 = previous term (which is 3)+ 6, 21 = previous term (which is 11)+ 6 + 4, 38 = previous term (which is 24) + 6 + 4×2, and so on. I am sure we can find a nice formula for subsequent terms of the sequence.
(Is there a way to embed LaTex in our comments?)
Comment by eldila
Made Tuesday, 26 of February , 2008 at 10:20 am
@Vishal
It appears you are on the correct path. I had a completely different method of analyzing this sequence. I will post it on thursday or friday. It is always interesting to see how different people solve the same problem.
Anyways, you can add latex comments by using the tag [ tex ] [ /tex ] (with the spaces removed)
