Please give the next 3 terms of this sequence with the formula or explanation, if possible:
1, 1, 2, 3, 5, 7, 11, 15, 22, 30......etc.
I thank you for any help.
if 1,1 is 1 then 22, to 30 is 8, then 1+8 is 9 so 9/ the total amount of terms 9/10 is .8333 which if you put in the granula formula you get 5 so the next term is 35
The next terms are: 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77.......etc.
This is the series of the sums of "partitions" of counting numbers from 1, 2, 3, 4.....etc.
The calculations of these numbers are arrived at by a very advanced and complicated "Partition Formula" of "Hardy, Ramanajun and Radamacher". It essentially calculates the number of ways any particular whole number can be added. Example:
Partitions of number 4, or P(4) = 4, 3+1, 2+1+1, 2+2, 1+1+1+1 =5 ways you can make up number 4. They quickly become very large as you go up the numbers. For P(200) = 3,972,999,029,388 !!.
I hope that helps.
