def is_triangle(triangle: int):
    """any tn in triangle sequence is t = ½n(n+1):
    Solving with quadratic formula reveals n is only an integer if (1+8t) ** 0.5 is an integer and odd"""
    if int((1+8*triangle)**0.5) == (1+8*triangle)**0.5 and ((1+8*triangle)**0.5)%2 == 1:
        return True
    return False