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

[some_letters]

Homework Statement

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

Homework Equations

I haven't any idea

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.