Counting constitutional isomers

The number of alkene constitutonal isomers for a particular carbon skeleton depends on
the number of different bonding environments for carbon AND
the number of adjacent pairs of carbon atoms where both are involved in three or fewer bonds to other carbon atoms.

When assessing the number of different bonding environments, it is important to realise that for this purpose

any linear chain is symmetrical about its centre,
thus bonding enviroments for carbon are the same to the left and the right of the centre.  
 
CCCC
C = C – C – C
C – C = C – C
Thus, for a four carbon chain, there are two alkene isomers.  
One has a double bond between red and blue carbons.
One with a double bond between the two blue carbons.. 
 
for branched carbon skeletons, 
branches of the same composition bonded to the same carbon are equivalent.
 C
 |
C  — C — C
 
There is only one C4 branched alkene isomer because all carbons adjacent to the central one are equivalent.

 
When assessing the number of adjacent pairs of carbon atoms where both carbons have three or fewer bonds to other carbons, it is important to realise that
a carbon with four carbons attached cannot be involved in a double bond.
 
A doubly-bonded carbon may be attached to a maximum of three other carbons.