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 A137503 Number of Frobenius equivalence classes of size n over GF(2^n) with their trace equal to the trace of their inverse. 0
 1, 0, 1, 4, 3, 8, 16, 28, 45, 96, 167, 308, 579, 1100, 2018, 3852, 7280, 13776, 26133, 49996, 95223, 182248, 349474, 671176, 1289925, 2485644, 4793355, 9255700, 17894421, 34638296, 67105714, 130148812, 252644985, 490852972 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,4 COMMENTS The number of Frobenius equivalence classes (FEC) of size n is given by A001037. The trace of an FEC of size n is the sum of its elements. The trace of (an element of) an FEC with a size d < n is either 0 or the sum of its elements; it is 0 when n/d is even; more generally, Tr(FEC) = Tr(representative) = n/d * sum of all elements in FEC. The number of FEC with size n and trace 1 is given by sequence A000048. The number of FEC with size n that is its own inverse (7 in the example below) is zero for odd n and A000048 (with n/2 as index) for even n. The number of FEC with size n that are their own inverses and have trace 1 is zero if n is odd, is equal to (this sequence with index n/2)/2 if n/2 is odd and equal to (this sequence with index n/2 + A000048 with index n/4)/2 if n/2 is even. LINKS Carlo Wood, Cracking parameter b of the elliptic curve. FORMULA Let b(1) = 0, b(2) = 1, b(n) = 2^(n-1) - b(n-1) - 2 * b(n-2) - 3. Let c(1) = 1, c(n) = 2^(n-1) - sum_{0

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Last modified April 10 16:16 EDT 2021. Contains 342845 sequences. (Running on oeis4.)