In theory, the primary sequence of a polypeptide will determine the folding of that polypeptide completely.  Therefore, an alpha-helical structure should not be able to form a beta-pleated strcuture and vice versa.  However, our methods of ab initio protein structure prediction are not yet good enough to be able to fully predict protein structure from primary sequence.  Despite the shortcomming in protein structure prediction, there are some general guidelines to differentiate between alpha-helical sequences and beta-sheets.

Since alpha-helices are more compact than beta-sheets, sequences with few bulky groups are more likely to form alpha-helices whereas sequences with many bulky groups are more likely to form beta-sheets.  Many adjacent bulky groups or bulky groups spaced 3-4  residues apart (directly above each other or below in the helix) will disfavor helix formation.  The same goes with residues of the same charge.  Because of the sterics of helices, glycines and prolines disfavor helix formation, although there are notable exceptions (e.g. collagen fibers which consist of mostly glycine and hydroxyproline).

Amphipaticity (spatial separation of hydrophobic and hydrophillic groups) will also favor the formation of secondary-structures.  For a helix, spacing hydrophobic groups 3-4 residues apart will create an amphipathic helix, while having hydrophobic residues at every other residue will create an amphipathic beta-sheet.

Put in another way, can the same polypeptide take on the alpha-helix structure under certain conditions, and yet take on the beta-pleated structure under other conditions?

Taking the spider web fluid proteins as an example this can happen. Inside the spider the filaments exist as alpha helices and change their conformation to a beta pleated sheets when used to build a spider web, due to dehydration.

Reviewing some of the posts I noticed this one.  This is an interesting question to me.  

Can a protein with the same AA sequence have a different shape?

This question brought up Prion theory.  The PrP protein.  PrP stands for prion-related protein.  It earned Prusiner the 1997 Nobel.  The normal protein found in humans changes shape when in contact with the PrP protein.  

I have enclosed the shapes.  

Notice that the normal protein has more alpha-helixes than the prion protein which has more beta sheets.

Normal on the left, abnormal on the right

My post wasn't a question, just an example for the initial post.