What is the next number in the following series?

1, 2, 4, 13, 31, 112, ?

(In reply to

by V)

Well I got the same answer as you. Except I had a different approach, I added 1^2 to the first number(1), then I added 2(1^2) to the sum of 1+1^2, then I multiplied the base of the previous square by 3 making it 3^2, then added that to the sum of 1+1^2+2(1^2) then I added 2(3^2) to that sum. I continued this process, coming to an answer of 274. Basically its (1)+1^2=(2)+2(1^2)=(4)+(3^2)=(13)+2(3^2)=(31)+(9^2)=(112)+2(9^2)=(274),if you wanted to continue the sequence it would be (274)+(27^2)=(1003)+2(27^2)=(2461) so on and so on. The only problem with your approach, I'm not totally sure if you would know what number to add by after multiplying 274 by 2. And I'm 16.