How can I remove those duplicate sequence in UNIX?What command line I should type?

The input is:
>HWI-EAS382_30FC7AAXX:4:1:1580:1465
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
>HWI-EAS382_30FC7AAXX:4:1:1062:1640
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
>HWI-EAS382_30FC7AAXX:4:1:272:629
AAAAAAAAGCTATAGTCTCGTCACACATACTCACAA
>HWI-EAS382_30FC7AAXX:4:1:1033:1135
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
>HWI-EAS382_30FC7AAXX:4:1:1421:27
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

My desired output is:
>HWI-EAS382_30FC7AAXX:4:1:1580:1465
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
>HWI-EAS382_30FC7AAXX:4:1:272:629
AAAAAAAAGCTATAGTCTCGTCACACATACTCACAA

What command line I should type to remove those duplicated sequence?
Thanks for all of your advise.

Something like this?

awk '/>/{s=$0;next}!a[$0]++{print s;print}' file

Regards

awk '!x[$0]++' FILE

Hi, fajohnson...
Your command line is worked. But still left all the header of the nucleotide sequence. Do you have better idea that I just remain the first header of those same nucleotide sequence?
My input:
>HWI-EAS382_30FC7AAXX:4:1:631:449
>HWI-EAS382_30FC7AAXX:4:1:93:1407
>HWI-EAS382_30FC7AAXX:4:1:154:1123
>HWI-EAS382_30FC7AAXX:4:1:912:1008
>HWI-EAS382_30FC7AAXX:4:1:57:316
>HWI-EAS382_30FC7AAXX:4:1:1287:1193
>HWI-EAS382_30FC7AAXX:4:1:1451:1559
>HWI-EAS382_30FC7AAXX:4:1:1431:1913
TTTCCGCGAACTGCAAAAGACGTTTCGTATGCCGTT

My output just want left this:
>HWI-EAS382_30FC7AAXX:4:1:631:449
TTTCCGCGAACTGCAAAAGACGTTTCGTATGCCGTT

Thanks for your advise. Have a nice day.

Try this:

awk '/^>/{if(hdr=="") hdr=$0}/^[^>]/{x[$0]++;if(x[$0]==1) {print hdr;print} hdr=""}' infile