Von Neumann Neighborhood

APL (Dyalog Extended), 23 bytes

-4 thanks to ovs.

Anonymous tacit infix function, taking coordinates of a cell and radius as left and right arguments. Requires 0-based indexing.

{⍺∘+¨⍵-⍸⍵≥+/¨|∘.,⍨⍵…-⍵}

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{} "dfn"; left argument is and right argument is :

⍵…-⍵ inclusive integer range from radius to negative radius

∘.,⍨ Cartesian selfie product

⊢m← assign to m and pass that

| absolute values

+/¨ sum each (gives matrix of Manhattan distances)

⍵≥ indicate which ones are less than or equal to the radius

ɩndices where true

⍵- subtract from radius

⍺∘+¨ add the cell coordinates to each


05AB1E, 14 13 bytes

-1 thanks to ovs

D(ŸãʒÄO¹[email protected]}€+

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Takes input as range, coordinates

Explanation:

D duplicate the range in the stack
( negate
Ÿ push the range [-range..range]
ã Cartesian power
 ʒ filter
  Ä absolute value, vectorizes over each of the coordinates
   O sum - distance from 0,0
    ¹[email protected] less than or equals to the range
 } end filter
€ map
+ add, with the implicit center coordinate

Perl 5, 64 bytes

sub n($x,$y,$d){map{//;map[$x+$',$y+$_],-$d+abs..$d-abs}-$d..$d}

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Saved 4 bytes, thanks to Xcali.