A136608 (1/576)*number of ways to express n as the determinant of a 4 X 4 matrix with elements 1...16.

14392910, 1550244, 2188523, 2029381, 2828486, 1905576, 2901300, 1813327, 3097897, 2169409, 2695559, 1697839, 3767494, 1682771, 2548638, 2503246, 3286048, 1684275, 3093051, 1655317, 3500693, 2374117, 2403536, 1619568

Offset: 0

Author

Hugo Pfoertner, Jan 21 2008

Keywords

• fini
• nonn

Comments

0 can be expressed in a(0)*(4!)^2=8290316160 ways as the determinant of a 4 X 4 matrix which has elements 1...16. One such way is e.g. det ((1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16))=0. All numbers between -38830 and +38830 can be expressed by such a determinant. The first number not expressible is given by A088216(4). The largest expressible number is given by A085000(4)=40800.

Examples

			a(40800)=1 because the only 4X4 matrices with elements 1...16 with the determinant 40800 are the 576 combinations of determinant-preserving row and column permutations of ((16 6 4 9)(8 13 11 1)(3 12 5 14)(7 2 15 10)).
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 0..40800
• Hugo Pfoertner, Illustration of occurrence counts. (Zoom into diagram to see details)
• Hugo Pfoertner, Illustration of occurrence counts. Upper range.

Crossrefs

Cf. A088237 [numbers not expressible by 4X4 determinant], A088215, A088216, A085000, A136609.