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# Java, 65 bytes

Golfed:

    n->{int a=1,b=2;for(;n>0;--n){b=a-b;a-=b;}System.out.println(a);}

This uses the standard trick of calculating Fibonacci using only two variables to hold the state, but modified to work with subtraction. I am aware that theoretically, `System.out.print()` _should_ work here but in practice it is inconsistent with flushing output and sometimes (often enough to be an issue) will literally print _nothing_ using the Oracle JVM.

This function is zero-indexed.

Ungolfed:

    public class FibtractionFibonacciButWithSubtraction {
      public static void main(String[] args) {
        for (int i : new int[] { 1, 2, 11, 14, 21, 24, 31 }) {
          f(n -> {
            int a = 1, b = 2;
            for (; n > 0; --n) {
              b = a - b;
              a -= b;
            }
            System.out.println(a);
          } , i);
        }
      }
    
      private static void f(java.util.function.Consumer<Integer> function, int n) {
        function.accept(n);
      }
    }