# Neighbour Points in N-Dimensional Space

if you got a integer point in the n-dimensional space how many neighbor integer points does it have?

1D you have 2

2D you have 8

3D you have 26

i came to the formula $$n_i = 2*(n_{i-1}+1)+n_{i-1} = 3 * n_{i-1} + 2$$ What is the closed form for n-dimension?

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$3^n-1$
I.e., the $3\times 3 \times 3 \times ...$ cube minus the point in the middle.