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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). 6

%I #19 Jun 09 2018 15:18:30

%S 86,104,172,252,332,412,492,572,652,732,812,892,972,1053,1134,1215,

%T 1296,1377,1458,1539,1620,1701,1782,1863,1944,2025,2106,2187,2268,

%U 2349,2430,2511,2592,2673,2754,2835,2916,2997,3078,3159,3240,3321,3402,3483,3564

%N 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).

%F 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]

%e 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.

%t 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 *)

%Y 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).

%K nonn

%O 0,1

%A _Hugo Pfoertner_, Aug 19 2004

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