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Perfect Squares Without Borders
Given n=m^2, return a list of integers that do not border the m x m grid of integers from 1 to n.
Examples
n=1 (m=1)
Grid:
[1]
Return:
[]
n=4 (m=2)
Grid:
[1,2]
[3,4]
Return:
[]
n=9 (m=3)
Grid:
[1,2,3]
[4,5,6]
[7,8,9]
Return:
[5]
n=16 (m=4)
Grid:
[ 1, 2, 3, 4]
[ 5, 6, 7, 8]
[ 9,10,11,12]
[13,14,15,16]
Return:
[6,7,10,11]
For higher values of m, this answer does a great visualization.
Rules:
You may take in either m or n (where n = m*m).
If taking in n you may have undefined behavior where there exists no m for n (E.G. 15).
n > 0, m > 0: Both must be integer values.
The output may be as a 1D/2D array, matrix or whitespace delimited
The output must be in order from least to greatest.
If outputting as a matrix this means it must be as it would be in the grid.
This is codegolf, lowest bytecount wins.
C, 50 bytes
i;f(m){for(i=m;++i
Try it online!
Pure Bash, 49
The boring answer:

C, 50 bytes
i;f(m){for(i=m;++i
1&&printf("%d ",i);} Try it online!
20180202 21:36:32 
Pure Bash, 49
The boring answer:
for((i=$1;i++<$1*$1$1;));{ ((i%$1>1))&&echo $i;}
Try it online.
Or the interesting answer for 52:
(($1>2))&&eval echo \$[$1*{1..$[$12]}+{2..$[$11]}]
Try it online.
20180202 21:47:15 
Haskell, 31 bytes
f m=[ii<[m..m*mm],mod i m>1]
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20180202 21:51:08 
Octave, 31 bytes
@(m)vec2mat(1:m*m,m)(2:m,2:m)
Returns a matrix.
Try it online!
20180202 21:54:56 
Jelly, 8 bytes
sÆ½ḊṖ$⁺€
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20180202 21:55:11 
R, 44 bytes
function(m)matrix(1:m^2,m,m,T)[m,m][1,1]
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Returns a matrix.
Generates a matrix, then removes the last row and column with [m,m], then removes the first row and column [1,1].
20180202 22:06:16 
05AB1E, 9 bytes
LItä¦¨ε¦¨
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20180202 22:10:03 
Python 2, 44 bytes
lambda t:[k for k in range(t,~t*t)if k%t>1]
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I promise this is my last answer (to this challenge) today. Takes m as input.
20180202 22:12:34 
Bash + GNU utilities, 35
seq $1 $[$1*$1$1]sed 1~$1d\;2~$1d
Try it online.
20180202 22:22:59 
Pyth, 10 bytes
mtPdtPcQS*
Try it here!
Takes m as input.
20180202 22:24:00 
J, 23 bytes
[::@}:@}.^:2@%:]\1+i.
Takes n as input, returns a matrix
How it works
1+i.  generates a list 1..n
@%:  finds the square root of n and negates it (m)
]\  makes a table (matrix) m x m from the list
^:2  do the following twice:
:@}:@}.  drop the first row, then drop the last row, then transpose
[:  cap the fork
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20180202 22:33:30 
Java 8, 241 bytes
j>{if(j<9)return new int[1];int q=(int)Math.sqrt(j);int w=(q2)*(q2);int[]e=new int[w];int[][]r=new int[q][q];int t=0;int y=0;for(int i=1;i
1&&i
1&&p
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Java makes it very tough(lots of bytes) when you have to create an array of somewhat "unknown" size.
This answer needs to be cleaned up, a lot, but I revisit later tonight.
20180202 22:39:17 
Proton, 28 bytes
k=>filter(u=>1
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Takes m as input.
How?
Filters the integers in [k, k2k) that, when divided by k, yield a remainder higher than 1. This ensures that both ends are trimmed, because the first one yields 0 and the last one yields 1. It is also guaranteed to return a higher value for any valid integer, because they are consecutive.
20180202 22:44:45 
Jelly, 8 bytes
Ṗ×+€ṖṖḊ€
A monadic link taking m and returning a list of lists (the inner rows).
Try it online!
How?
Ṗ×+€ṖṖḊ€  Link m e.g. 5
Ṗ  pop m (implicit range) [1,2,3,4]
×  multiply by m [5,10,15,20]
Ṗ  pop m again [1,2,3,4]
+€  add €ach [[6,7,8,9],[11,12,13,14],[16,17,18,19],[21,22,23,24]]
Ṗ  pop the last item [[6,7,8,9],[11,12,13,14],[16,17,18,19]]
Ḋ€  dequeue €ach [[7,8,9],[12,13,14],[17,18,19]]
20180202 22:54:11 
Red, 63 bytes
f: func[n][repeat i(n  2 * n)[if n + i // n > 1[print n + i]]]
This is a Red port of Mr. Xcoder's Python 2 solution
Try it online!
20180202 22:57:04