https://oeis.org/A118141

"A parity pattern is a matrix of 0's and 1's with the property that every 0 is 
adjacent to an even number of 1's and every 1 is adjacent to an odd number of 
1's."

As a J exercise, I've defined a verb that creates a parity pattern when given 
its height and the first row.

   tripsums=: 3: +/\ (0&, @: ,&0)
   nextrow=: 2: | (+ tripsums)
   grow=: , _2&{ nextrow {:
   addzeros=: ,:~ ~:~
   paritypattern=: ([: }. grow@:]^:(<: @: [)) addzeros
   4 paritypattern 0 0 1 1
0 0 1 1
0 1 0 0
1 1 0 1
0 1 0 1

I would love to see other approaches to this problem.

- Ivan
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