A097399 Maximum of the determinant over all permutations of the entries of a 3 X 3 matrix which are consecutive integers in the range (n-4,n+4).

86, 104, 172, 252, 332, 412, 492, 572, 652, 732, 812, 892, 972, 1053, 1134, 1215, 1296, 1377, 1458, 1539, 1620, 1701, 1782, 1863, 1944, 2025, 2106, 2187, 2268, 2349, 2430, 2511, 2592, 2673, 2754, 2835, 2916, 2997, 3078, 3159, 3240, 3321, 3402, 3483, 3564

Offset: 0

Author

Hugo Pfoertner, Aug 19 2004

Keywords

• nonn

Examples

			a(0)=86 because the maximal determinant that can achieved using the consecutive integers -4,-3,-2,-1,0,1,2,3,4 as matrix elements of a 3 X 3 matrix is det((-4,-3,0),(1,-1,4),(-2,3,2))=86. Another example for a(5)=412 is given in A085000.
		

Crossrefs

Cf. A097400 = corresponding number of different determinants, A097401, A097693 = maximum of determinant if distinct matrix elements are selected from given range, a(5)=A085000(3) maximal determinant with elements (1..n^2).

Programs

Mathematica

Join[{86,104,172,252,332,412,492,572,652,732,812,892},LinearRecurrence[ {2,-1},{972,1053},40]] (* or *) Table[ Det[ Partition[ #,3]]&/@ Permutations[ Range[n-4,n+4]]//Max,{n,0,45}] (* Harvey P. Dale, Jan 14 2015 *)

Formula

G.f.: (x^13+12*x^3+50*x^2-68*x+86) / (x-1)^2. [Colin Barker, Dec 13 2012] [I suspect this is merely a conjecture. - N. J. A. Sloane, Jun 09 2018]