Sum of edge numbers for triangle given starting number, increment and number of levels

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For example, if starting number (N) = 1, increment (I) = 5, and number of levels (L) = 4, you get the following triangle:

16 11 11 6 6 1 1

Sum = 1 + 6 + 11 + 16 + 11 + 6 + 1 = 52

Another example, with N = 30, I = -4, L = 3 gives:

30 30 26 26 22

Sum = 30 + 26 + 22 + 26 + 30 = 134

If L = 1, there is only a single number in the triangle, which is N.

What equation can will give the sum of the edge and works for all: N, I (including negative), L (including 1) ?

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$S=N+(N+I)+(N+2I)+...+[N+(L-1)I]+...+(N+I)+N=$ $\boxed{S=(2L-1)N+(L-1)^2I}$

Ex1: $S=(2.4-1).1+(4-1)^2.5=7+45=52$

Ex2: $S=(2.3-1).30+(3-1)^2.(-4)=150-16=134$