Find the Value of $a_{2008}$ in the Sequence

[Albert1]

A sequence as follows :
$0,1,-1,2,3,-2,4,5,6,-3,7,8,9,10,-4,11,12,13,14,15,16,-5,--------$
please find :$a_{2008}=?$

 

[kaliprasad]

A sequence as follows :
$0,1,-1,2,3,-2,4,5,6,-3,7,8,9,10,-4,11,12,13,14,15,16,-5,--------$
please find :$a_{2008}=?$

are you sure that 16 is there

 

[Albert1]

are you sure that 16 is there

I am sure that 16 is there .
if 16 is not there , then this question will be much easier

 

[Albert1]

A sequence as follows :
$0,1,-1,2,3,-2,4,5,6,-3,7,8,9,10,-4,11,12,13,14,15,16,-5,---------$
please find :$a_{2008}=?$

hint:

Spoiler

we have 1 number after 0
2 numbers after -1(2-3)
3 numbers after -2(4-6)
4 numbers after -3(7-10)
6 numbers after -4(11-16)
and it should have 9 numbers after -5(17-25)
can you figure out the regular pattern?

more hint:

Spoiler

$a_n+a_{n+2}=a_{n+3} \forall n\geq 1$
here we set $a_1=1,a_2=2,a_3=3, a_4=4,a_5=6...$

 

[Albert1]

A sequence as follows :
$0,1,-1,2,3,-2,4,5,6,-3,7,8,9,10,-4,11,12,13,14,15,16,-5,--------$
please find :$a_{2008}=?$

Spoiler

[FONT=&#26032]　[/FONT]	[FONT=&#26032]　[/FONT]	[FONT=&#26032]　[/FONT]	[FONT=&#26032]n[/FONT]	[FONT=&#26032]an[/FONT]
[FONT=&#26032]0[/FONT]	[FONT=&#26032]1[/FONT]	[FONT=&#26032]1[/FONT]	[FONT=&#26032]2[/FONT]	[FONT=&#26032]1[/FONT]
[FONT=&#26032]-1[/FONT]	[FONT=&#26032]2-3[/FONT]	[FONT=&#26032]2[/FONT]	[FONT=&#26032]5[/FONT]	[FONT=&#26032]3[/FONT]
[FONT=&#26032]-2[/FONT]	[FONT=&#26032]4-6[/FONT]	[FONT=&#26032]3[/FONT]	[FONT=&#26032]9[/FONT]	[FONT=&#26032]6[/FONT]
[FONT=&#26032]-3[/FONT]	[FONT=&#26032]7-10[/FONT]	[FONT=&#26032]4[/FONT]	[FONT=&#26032]14[/FONT]	[FONT=&#26032]10[/FONT]
[FONT=&#26032]-4[/FONT]	[FONT=&#26032]11-16[/FONT]	[FONT=&#26032]6[/FONT]	[FONT=&#26032]21[/FONT]	[FONT=&#26032]16[/FONT]
[FONT=&#26032]-5[/FONT]	[FONT=&#26032]17-25[/FONT]	[FONT=&#26032]9[/FONT]	[FONT=&#26032]31[/FONT]	[FONT=&#26032]25[/FONT]
[FONT=&#26032]-6[/FONT]	[FONT=&#26032]26-38[/FONT]	[FONT=&#26032]13[/FONT]	[FONT=&#26032]45[/FONT]	[FONT=&#26032]38[/FONT]
[FONT=&#26032]-7[/FONT]	[FONT=&#26032]39-57[/FONT]	[FONT=&#26032]19[/FONT]	[FONT=&#26032]65[/FONT]	[FONT=&#26032]57[/FONT]
[FONT=&#26032]-8[/FONT]	[FONT=&#26032]58-85[/FONT]	[FONT=&#26032]28[/FONT]	[FONT=&#26032]94[/FONT]	[FONT=&#26032]85[/FONT]
[FONT=&#26032]-9[/FONT]	[FONT=&#26032]86-126[/FONT]	[FONT=&#26032]41[/FONT]	[FONT=&#26032]136[/FONT]	[FONT=&#26032]126[/FONT]
[FONT=&#26032]-10[/FONT]	[FONT=&#26032]127-186[/FONT]	[FONT=&#26032]60[/FONT]	[FONT=&#26032]197[/FONT]	[FONT=&#26032]186[/FONT]
[FONT=&#26032]-11[/FONT]	[FONT=&#26032]187-274[/FONT]	[FONT=&#26032]88[/FONT]	[FONT=&#26032]286[/FONT]	[FONT=&#26032]274[/FONT]
[FONT=&#26032]-12[/FONT]	[FONT=&#26032]275-403[/FONT]	[FONT=&#26032]129[/FONT]	[FONT=&#26032]416[/FONT]	[FONT=&#26032]403[/FONT]
[FONT=&#26032]-13[/FONT]	[FONT=&#26032]404-592[/FONT]	[FONT=&#26032]189[/FONT]	[FONT=&#26032]606[/FONT]	[FONT=&#26032]592[/FONT]
[FONT=&#26032]-14[/FONT]	[FONT=&#26032]593-869[/FONT]	[FONT=&#26032]277[/FONT]	[FONT=&#26032]884[/FONT]	[FONT=&#26032]869[/FONT]
[FONT=&#26032]-15[/FONT]	[FONT=&#26032]870-1275[/FONT]	[FONT=&#26032]406[/FONT]	[FONT=&#26032]1291[/FONT]	[FONT=&#26032]1275[/FONT]
[FONT=&#26032]-16[/FONT]	[FONT=&#26032]1276-1870[/FONT]	[FONT=&#26032]595[/FONT]	[FONT=&#26032]1887[/FONT]	[FONT=&#26032]1870[/FONT]
[FONT=&#26032]-17[/FONT]	[FONT=&#26032]1871-1990[/FONT]	[FONT=&#26032]120[/FONT]	[FONT=&#26032]2008[/FONT]	[FONT=&#26032]1990[/FONT]