Found a series problem online, extremely hard to solve. help

some_letters

1. The problem statement, all variables and given/known data


What is the next number in the following series?
1 2 12 48 216 936 4104 17928 78408 342792 ____________

2. Relevant equations
I haven't any idea


3. The attempt at a solution

power's of two, powers of three, prime numbers. I am beat

it can be found on this test --->http://www.mental-testing.com/

Mod's, I am sorry if this is in the wrong sub-directory. I couldn't figure out where else to put it.

cepheid

All the numbers except the first two are divisible by 3.

Start with the first two numbers in the sequence (1 and 2) as being given.

Take 1 and double it: you get 2.

Add this to 2: you get 4.

Multiply the result by 3: you get **12**

Repeat these three steps over and over again, just shifting your position in the sequence forward by one number each time. For example:

2*2 = 4
4 + 12 = 16
16 * 3 = **48**

12*2=24
24+48 =72
72*3 = **216**

48*2 = 96
96+216= 312
312*3 = **936**

etc.

More generally, if a_i is the i^th number in the sequence, with a₁ = 1 and a₂ = 2, then:

a_i = 3 [2*a_i-2 + a_i-1 ] for i ≥ 3

a_i = 6a_i-2 + 3a_i-1

EDIT: and by the way, "Pre-calculus Mathematics" would have been a good sub forum to post this thread in since 1) it is mathematics and 2) it is the type of math that comes before learning calculus.

EDIT 2: based on this, I predict the next number in the sequence to be 1,498,824

Borek

In the past similar questions landed in the brain teasers.

cepheid

Good point Borek, especially since it didn't really seem like homework (else I would not have posted a full solution!)

some_letters

Thanks Cehpeid, I realized that every number was divisble by 2,3, and 12. I never thought to include the previous two terms.