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from sympy.ntheory import npartitions


def test_partitions():
    assert [npartitions(k) for k in range(13)] == \
        [1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77]
    assert npartitions(100) == 190569292
    assert npartitions(200) == 3972999029388
    assert npartitions(1000) == 24061467864032622473692149727991
    assert npartitions(2000) == 4720819175619413888601432406799959512200344166
    assert npartitions(10000) % 10**10 == 6916435144
    assert npartitions(100000) % 10**10 == 9421098519

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