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

Author

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

Keywords

• nonn

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

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)).