A136608 -id:A136608 - cp's OEIS frontend

A088215 (1/36)*number of ways to express n as the determinant of a 3 X 3 matrix with elements 1..9.

76, 32, 18, 30, 14, 47, 30, 25, 10, 41, 20, 42, 32, 25, 16, 36, 14, 31, 39, 28, 35, 39, 20, 22, 18, 33, 19, 45, 12, 21, 37, 26, 15, 41, 25, 37, 29, 27, 18, 34, 22, 24, 23, 24, 17, 48, 16, 16, 18, 15, 25, 35, 16, 21, 36, 43, 11, 30, 5, 18, 31, 17, 13, 28, 11, 42, 35, 24, 13, 35

Offset: 0

Hugo Pfoertner, Sep 23 2003

0 can be expressed in 36*76=2716 ways as the determinant of a 3 X 3 matrix which has elements 1..9. One such way is e.g. det ((1 2 3)(4 5 6)(7 8 9))=0. All numbers between -323 and +323 can be expressed by such a determinant. The first number not expressible is given by A088216.

Hugo Pfoertner, Table of n, a(n) for n = 0..412 [Gives all terms]
Hugo Pfoertner, Possible determinants of 3 X 3 matrix with elements 1..9.

Cf. A085000, A088214, A088216, A088217.

Cf. A136608 [analogous sequence for 4 X 4 matrices].

A136609 (1/(n!)^2) * number of ways to arrange the consecutive numbers 1...n^2 in an n X n matrix with determinant = 0.

Original entry on oeis.org

0, 0, 76, 14392910

Offset: 1

Hugo Pfoertner, Jan 21 2008

The computation of a(5) seems to be currently (Jan 2008) out of reach (compare with A088021(5)).

			a(1)=0 because det((1))/=0, a(2)=0, because the only possible determinants of a matrix with elements {1,2,3,4} are +-2, +-5 and +-10.

Cf. A001044, A046747, a(3)=A088215(0), a(4)=A136608(0), A221976.

cp's OEIS Frontend

A088215 (1/36)*number of ways to express n as the determinant of a 3 X 3 matrix with elements 1..9.

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