A353211 a(n) is the number of diagonalizable 2 X 2 matrices over GF(prime(n)).
8, 39, 305, 1183, 7271, 14209, 41633, 64999, 139679, 353249, 461311, 936433, 1412081, 1708519, 2438783, 3943889, 6056999, 6921121, 10073383, 12703391, 14196529, 19471999, 23725799, 31367249, 44260033, 52025201, 56270239, 65534183, 70573249, 81517409, 130064383, 147241511, 176128433, 186640999
Offset: 1
Keywords
Examples
a(2) = 8 because there are 8 diagonalizable 2 X 2 matrices over GF(2). They are: 1. [[0,0],[0,0]]. 2. [[0,0],[0,1]]. 3. [[1,0],[0,0]]. 4. [[1,0],[0,1]]. 5. [[1,0],[1,0]]. 6. [[0,0],[1,1]]. 7. [[0,1],[0,1]]. 8. [[1,1],[0,0]].
Links
- Lars Felix Lerner, Diagonalizable matrices over finite fields
Crossrefs
Subsequence of A101374.
Programs
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PARI
a(n) = my(p=prime(n)); (p^4 - p^2 + 2*p)/2; \\ Michel Marcus, May 01 2022
Formula
a(n) = (prime(n)^4 - prime(n)^2 + 2*prime(n))/2 = A101374(prime(n)).