This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A097693 #16 Aug 20 2025 06:25:30 %S A097693 86,216,438,776,1254,1896,2726,3768,5046,6584,8406,10536,12998,15816, %T A097693 19014,22616,26646,31128,36086,41544,47526,54056,61158,68856,77174, %U A097693 86136,95766,106088,117126,128904,141446,154776,168918,183896,199734 %N A097693 Largest achievable determinant of a 3 X 3 matrix whose elements are 9 distinct integers chosen from the range -n...n. %H A097693 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1). %F A097693 An optimal choice and arrangement is of the following form: det((-n, 1-n, n-4), (n-3, 3-n, n), (2-n, n-1, n-2))=2*(2*n^3-7*n^2+6*n+3). There are 35 other equivalent arrangements corresponding to permutations of rows and columns. %F A097693 G.f.: 2*x^4*(43-64*x+45*x^2-12*x^3)/(1-x)^4. - _Colin Barker_, Mar 29 2012 %e A097693 a(5)=216 because no larger determinant of a 3 X 3 integer matrix b(j,k) with distinct elements -5<=b(j,k)<=5,j=1..3,k=1..3 can be built than det((-5,-4,1),(2,-2,5),(-3,4,3))=216. %Y A097693 Other maximal 3 X 3 determinants: Cf. A097399: 3 X 3 matrix filled with consecutive integers, A097401: 3 X 3 matrix filled with integers from 0...n, A097694, A097695, A097696: corresponding sequences for 4 X 4 matrices. %K A097693 nonn,easy %O A097693 4,1 %A A097693 _Hugo Pfoertner_, Aug 24 2004