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Triangle T(n,k) read by rows, where T(n,k) = number of times the determinant of a real n X n (0,1)-matrix takes the value k, for n >= 0, 0 <= k <= A003432(n).
4

%I #25 Apr 29 2024 10:53:10

%S 0,1,1,1,10,3,338,84,3,42976,10020,1200,60,21040112,4851360,1213920,

%T 144720,43560,3600,39882864736,9240051240,3868663680,768723480,

%U 418703040,63612360,46569600,6438600,5014800,529200,292604283435872

%N Triangle T(n,k) read by rows, where T(n,k) = number of times the determinant of a real n X n (0,1)-matrix takes the value k, for n >= 0, 0 <= k <= A003432(n).

%C The first 4 rows were provided by _Wouter Meeussen_.

%H Minfeng Wang, <a href="/A089478/b089478.txt">Table of n, a(n) for n = 0..118</a>

%e a(4) = T(2,1) = 3 because there are 3 different (0,1)-matrices with determinant=1:

%e ((1,0),(0,1)), ((1,1),(0,1)), ((1,0),(1,1)).

%e Triangle T(n,k) begins:

%e 0, 1;

%e 1, 1;

%e 10, 3;

%e 338, 84, 3;

%e 42976, 10020, 1200, 60;

%e 21040112, 4851360, 1213920, 144720, 43560, 3600;

%e ...

%o (Fortran)

%o c See link in A086264.

%Y Cf. T(n,0) = A046747(n), T(n,1) = A086264(n), T(n,A003432(n)) = A051752(n).

%Y The n-th row of the table contains A089472(n) nonzero entries.

%Y Cf. A089479.

%K nonn,hard,tabf

%O 0,5

%A _Hugo Pfoertner_, Nov 04 2003

%E Edited by _Alois P. Heinz_, Dec 20 2023