# [Python 2], <s>140</s> 137 bytes

<!-- language-all: lang-python -->

 n=input()
 x=[]
 a=[0]*n+[1]+n*[0]
 z=n%2
 exec'x+=[a];a=[(i%2^z)*sum(a[i-1:i+2])for i in range(2*n+1)];z^=1;'*n
 print map(sum,zip(*x))[1:-1]

[Try it online!] or [Try it online!](https://tio.run/nexus/python2#PYxLCsMgFAD3nuJtQvwF@izdGDyJGJBWi4u8BptA8PKpq@5mMTPXK2XInIRlcDofGETnb0GS8hgUyc4MmqPBMEhneo6ncj6GuVu8DGZpQn6PlUdfJrRFmSDyp0KBQlAjvRM3fYUizG1xOI@SGNS0H5VgjRvvqW5l4/IUwqOdMFz/vNB27FzYzIu4PGqj7/qhEcMP "Python 2 – TIO Nexus")


[Python 2]: https://docs.python.org/2/
[Try it online!]: https://tio.run/nexus/python2#DYzLCsMgEADvfoWXEB8NdD1G/BLZgBRb9pCt2ATEn7fe5jAzgwNxuS@lRQsRRQrxiYZtBLRsJoseeHEit/xamw0xoZ@OosUdXZvffaoUaYOdrEP9/lZJkljWxJ@s3ByBRt@PAH41LEolvuSZiprho1NRpmkdYd8AxwD4Aw "Python 2 – TIO Nexus"

<sup>For `n=3`</sup> 
Starts with a list with `n` zeros surround an one - `[[0, 0, 0, 1, 0, 0, 0]]` 
Generate the full pyramid

 [[0, 0, 0, 1, 0, 0, 0],
 [0, 0, 1, 0, 1, 0, 0],
 [0, 1, 0, 2, 0, 1, 0]]

Rotate 90º and sum each row, discarding the first and the last one (only zeros)

 [[0, 0, 0],
 [0, 0, 1],
 [0, 1, 0],
 [1, 0, 2],
 [0, 1, 0],
 [0, 0, 1],
 [0, 0, 0]]