What is the series representation of the sequence 4,8,28,80?

Question

amistre64 · Answer

series representation?

amistre64 · Answer

like change from sequences to summation of sequence?

anonymous · Answer

Yeap!

amistre64 · Answer

i cant see a pattern that would be helpful in determing the sequence

amistre64 · Answer

any ideas?

anonymous · Answer

i dont have >.< i tried breaking it down by determining the factors. but still, can't see the pattern. :|

amistre64 · Answer

i take it the sequences represents the output of some power series/polynomial ....

amistre64 · Answer

maybe?

4 = c1
8 = c2x
28 = c3(x^2)/2
80 = c4(x^3)/6

anonymous · Answer

actually the representation i am trying to get is from 4x+8x^2+28x^3+80x^4

amistre64 · Answer

im getting confused in the terminology ...

anonymous · Answer

summation of sequences* sorry :D

amistre64 · Answer

if i read it right then; you need the "function" that creates these coeffs of this given power series ...

anonymous · Answer

$$\sum_{n=0}^{\infty} (the sequence of coefficient)\times x ^{n+1}$$ this should be the output i just dont know what to put in the coeff

amistre64 · Answer

yep, thats what my thoughts were .... eventually :)

anonymous · Answer

haha. sorry im really bad at expressing myself :D

amistre64 · Answer

im just wondering if we equate this to the formation of a maclaurin series .... at the moment

amistre64 · Answer

and its just the 4 terms of the sequence right?

anonymous · Answer

yes though it's up to inf

anonymous · Answer

my instructor told me to stop the iteration when i see a pattern! hahaha

amistre64 · Answer

4,8,28,80, ...  or is the "..." parts = 0?

anonymous · Answer

yes, that's that!

amistre64 · Answer

whaich part is right lol

anonymous · Answer

80,.....+n hahaha

amistre64 · Answer

4  8   28   80
  4  20  52
    16  32
       16

cant really say if this makes a good pattern to follow; i dont see enough number to say yes or no to

anonymous · Answer

80??

4, 8, 28..
is $$4\sum_{i=1}^{4} i ^{2} - 2$$

but 80 is not included

anonymous · Answer

4 8 28 80 244 728

amistre64 · Answer

.... how many numbers you holding back on ;)

anonymous · Answer

this is up to infinity!!

amistre64 · Answer

4  8   28   80   244  728
  4  20  52  164    484
    16  32  112  320
       16   80  208
           64  128
              64

i might see a pattern

anonymous · Answer

I got something...

1,2,7,20  is each number 3* previous plus minus 1 alternating

anonymous · Answer

That's after u factor out the 4..

anonymous · Answer

But that's not quite going to work with 244...

anonymous · Answer

Oh, yes it does....

amistre64 · Answer

4  8   28   80   244  728     [1532]  [5904]  any way to know if 
  4  20  52  164    484   1460   4372         these 2 are next?
    16  32  112  320   976    2912
       16   80  208   656   1936
           64  128   448 1280
              64   320   832
                 256   512
                     256

anonymous · Answer

I asked someone but she said that this is not an arithmetic/geometric sequence

anonymous · Answer

My sequence works....

anonymous · Answer

can you put it into the algebraic sequences? :D

anonymous · Answer

Sure, now there is a pattern, it must be possible...

anonymous · Answer

What's the thing for dealing with an alternating sign, I forgot....

amistre64 · Answer

(-1)^n

anonymous · Answer

That's it..:-)

anonymous · Answer

Thanks amistre and estudier. I am going to bed now. Hope I can figure this out by tomorrow morning.