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).
Original entry on oeis.org
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
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.
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).
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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 *)
A366158
Number of distinct determinants of 3 X 3 matrices with entries from {0, 1, ..., n}.
Original entry on oeis.org
1, 5, 25, 77, 179, 355, 609, 995, 1497, 2167, 2999, 4069, 5289, 6841, 8595, 10661, 13023, 15777, 18795, 22305, 26085, 30397, 35107, 40381, 45929, 52247, 58929, 66287, 74139, 82767, 91643, 101701, 112013, 123235
Offset: 0
Cf.
A058331 (distinct determinants for 2 X 2 matrices).
Cf.
A097400 (distinct consecutive entries in 3 X 3 matrix).
-
mat[n_Integer?Positive] := mat[n] = Array[m, {n, n}]; flatMat[n_Integer?Positive] := flatMat[n] = Flatten[mat[n]]; detMat[n_Integer?Positive] := detMat[n] = Det[mat[n]] // FullSimplify; a[d_Integer?Positive, 0] = 1; a[d_Integer?Positive, n_Integer?Positive] := a[d, n] = Length[DeleteDuplicates[Flatten[ParallelTable[Evaluate[detMat[d]], ##] & @@ Table[{flatMat[d][[i]], 0, n}, {i, 1, d^2}]]]]; Table[a[3, n], {n, 0, 9}]
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from itertools import product
def A366158(n): return len({a[0]*(a[4]*a[8] - a[5]*a[7]) - a[1]*(a[3]*a[8] - a[5]*a[6]) + a[2]*(a[3]*a[7] - a[4]*a[6]) for a in product(range(n+1),repeat=9)}) # Chai Wah Wu, Oct 06 2023
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