The nth triangular number is the sum of the first n positive integers. The sequence of triangular numbers starts 1, 3, 6, 10, 15, and 21. These numbers are involved in Cody Problems 5, 291, 44289, 44334, 44732, 55680, 55695, 55705, 55710, and 55715, for example.
Write a function to return the sum of the non-triangular numbers between the nth and (n+1)st triangular numbers. For example, if n = 3, then the function should return 7+8+9 = 24. Beware the banned functions.
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Chris Cleveland goc3 Pauli Huusari Lorenzo

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