doubt..counting the isoners

Some Golden Rules In Isomerism:
total number of geometrical isomers in polyenes
(1) 2ⁿ---->when terminal groups or atoms are different on both sides (n-->no of double bonds)(e.g. 2,4 heptadiene has 2²=4 isomers
(2) 2^n-1+2^{n/2 - 1}------->when terminal groups or atoms are same(e.g. 2,4 hexadiene has 2¹ + 2⁰ =3 isomers

total no of optical isomers of a compound

(1) when the molecule cannot be divided into equal halves and (n) is the number of asymmetric carbon atoms
number of (d) and (l) forms =(a)= 2ⁿ
number of meso forms = (m) =2⁰
total number of isomers = (a) +(m)

(2)when the molecule can be divided into equal halves
(i) (n)---->number of asymmetric carbon atoms is even
(d) and (l) isomers =(a) = 2^n-1
meso isomers =(m) = 2^{n/2 - 1}
total no of isomers = (a) +(m)

(ii) (n)------>number of asymmetric carbon atoms is odd
(d) and (l) isomers =(a) =2^n-1 - 2^{(n/2 - 1/2)}
meso isomers =(m) =2 ^{(n/2 -1/2)}
total number of isomers = 2^n-1

a good colection of formulae[6]
but i dont want all these...[2]
i just want to know how to calculate no. of isomers manually...