Times 3, cut in half, plus 1.
The next number is 75.
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Zero fits into the sequence of integers; it is exactly one less than the number one, and it is exactly one more than the number negative one. It is also an integer because it is not a fraction.
The differences are not the same so the sequence is not arithmetic. The sequence starts with a zero, so it cannot be geometric, or an exponential (power) sequence. The quartic: (2n4 - 19n3 + 64n2 - 83n + 36)/6 fits the 5 points. That gives the next term as 55.
It is possible to find a quartic equation (power 4) so that any fifth number is the next in the sequence. The cubic that fits these is Un = (n3 + 17n + 30)/6 for n = 1, 2, 3, ... and therefore, the next term is 40.
1, 4, 7, 10, 13, …