Create list of values with arbitrary index and the use it in a function

Question

I have the following generating functions:

$l_{2i-1}=l_{1}-(i-2)(w+s)$ with $i\geq 2$ and $l_{2i}=l_{2}-(i-1)(w+s)$ with $i\geq 2$, so the first one is for odd index and the second for even index. Then I need to use the two for a function, let´s say a sum, So i'm going to need $l_{1},l_2,l_3,...$ etc but these are generated from the two different functions, so how can I call the $l_{odd}$ using the first function and $l_{even}$ using the second function in the same sum ?

I tried simply defining my first function like f[2*i_-1] but it doesn´t work :(

Many thanks,

Answer 1

One way is to use OddQ and EvenQ. For example:

m[x_] := x^2 /; OddQ[x]
m[x_] := 5 x^3 /; EvenQ[x]

defines m differently for odd and even arguments. For your f, maybe something like

f[x_] := l1 - (x - 2) (w + s) /; OddQ[x]
f[x_] := l2 - (x - 1) (w + s) /; EvenQ[x]