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Can you find the next terms of 1,2,4,7,12,19,30,45,67,97,139....?
If you set a_0 = 1, a_1 = 2 etc, then a_k is the number of integer solutions of
x + 2y + 3v + .......+ <= k.
2 Answers
- 9 years agoFavorite Answer
This is just a cumulative sum of the number of integer partitions of the integers, starting at 0.
Wolfram alpha tells me that the number of integer partitions of 11 is 56, so the next element in the sequence is 195.
These numbers in the sequence get large. For example, the 300'th term in that sequence is 132510310832964143.
Had I not recognized your sequence anyway, a nice thing is the online encyclopedia of integer sequences. Just give it your sequence, and it will find the solution. oeis tells us it is the summatory function of the number of partitions of n.
Source(s): http://en.wikipedia.org/wiki/Partition_(number_the... http://www.wolframalpha.com/input/?i=number+of+par... http://oeis.org/wiki/Welcome http://oeis.org/w/index.php?title=Special%3ASearch...
