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A353211
a(n) is the number of diagonalizable 2 X 2 matrices over GF(prime(n)).
1
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
1,1
FORMULA
a(n) = (prime(n)^4 - prime(n)^2 + 2*prime(n))/2 = A101374(prime(n)).
EXAMPLE
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]].
PROG
(PARI) a(n) = my(p=prime(n)); (p^4 - p^2 + 2*p)/2; \\ Michel Marcus, May 01 2022
CROSSREFS
Subsequence of A101374.
Sequence in context: A144414 A045909 A264091 * A319362 A154425 A120931
KEYWORD
nonn
AUTHOR
STATUS
approved