Dear Sir. Concerning your issue about the number of amino acids that are needed to form a Beta sheet, alpha helix and coil. Alpha helix: has 3.6 amino acids per turn of the helix, which places the C=O group of amino acid #1 exactly in line with the H-N group of amino acid. In contrast to the alpha helical structure, Beta Sheets are multiple strands of polypeptides connected to each other through hydrogen bonding in a sheet-like array. Hydrogen bonding occurs between the NH and CO groups between two different strands and not within one strand, as is the case for an alpha helical structure. Due to its often rippled or pleated appearance, this secondary structure conformation has been characterized as the beta pleated sheet. The beta strands can be arranged in a parallel, anti-parallel, or mixed (parallel and anti-parallel) manner. I think the following below links may help you in your analysis:
Thanks dear sir, you know I was working on neural networks to predict protein secondary structure and the best sliding window was 5, which means to predict a secondary structure, we should at least have an input of 5 or 7 amino acids, but I'm not sure if this window is useful to predict beta sheets.
Alpha helix has 2 hydrogen bonds per one amino acids - except 4 terminal on each side which has 1 hydrogen bond per amino acid. Here is the formula say we have 20 amino acids (20x2- (4+4))/2=16 hydrogen bonds.
Here is a couple videos that I made on this topic:
How Alpha helix is formed https://youtu.be/_lmsb7iC1aA
How to calculate hydrogen bonds in Alpha Helix https://youtu.be/-lAdSzG2vRY