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A136608 (1/576)*number of ways to express n as the determinant of a 4 X 4 matrix with elements 1...16. 3
14392910, 1550244, 2188523, 2029381, 2828486, 1905576, 2901300, 1813327, 3097897, 2169409, 2695559, 1697839, 3767494, 1682771, 2548638, 2503246, 3286048, 1684275, 3093051, 1655317, 3500693, 2374117, 2403536, 1619568 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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.

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.

EXAMPLE

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)).

CROSSREFS

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

Sequence in context: A111346 A238080 A251009 * A205413 A186067 A183661

Adjacent sequences:  A136605 A136606 A136607 * A136609 A136610 A136611

KEYWORD

fini,nonn

AUTHOR

Hugo Pfoertner, Jan 21 2008

STATUS

approved

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Last modified September 18 06:35 EDT 2020. Contains 337166 sequences. (Running on oeis4.)