Skew(2^e) equals (7 times 4 to the e-2 plus 8) divided by 6 for e at least 3, with the recurrence Skew(2^e) = 4 times Skew(2^{e-1}) minus 4 for e at least 4.
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Enumeration of skew morphisms of cyclic $2$-groups
Skew(2^e) equals (7 times 4 to the e-2 plus 8) divided by 6 for e at least 3, with the recurrence Skew(2^e) = 4 times Skew(2^{e-1}) minus 4 for e at least 4.