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

1,1

Links

Table of n, a(n) for n=1..34.

Lars Felix Lerner, Diagonalizable matrices over finite fields

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

Adjacent sequences: A353208 A353209 A353210 * A353212 A353213 A353214

Keyword

nonn

Author

Lars Felix Lerner and Elias S. Cleusters, Apr 30 2022

Status

approved