A303262 - OEIS

%I #10 Apr 30 2018 11:42:51

%S 1,1,1,8,9,28,35,1,65,80,91,1,44,99,550,854,1936,2761,3421,3732,4043,

%T 4354,1,63,65,2527,3311,3969,4095,13545,13889,1,128,129,145,6066,

%U 16384,16385,16512,16513,16641,18560,18577,18669,18705,90738,103759,103965,109220,120142,121920

%N Table where row n lists numbers N equal to the determinant of an n X n circulant having as a row the base n+1 digits of N.

%e The table starts

%e (n=1) 1,

%e (n=2) 1,

%e (n=3) 1, 8, 9, 28, 35,

%e (n=4) 1, 65, 80, 91,

%e (n=5) 1, 44, 99, 550, 854, 1936, 2761, 3421, 3732, 4043, 4354,

%e (n=6) 1, 63, 65, 2527, 3311, 3969, 4095, 13545, 13889,

%e (n=7) 1, 128, 129, 145, 6066, 16384, 16385, 16512, 16513, 16641, 18560, 18577, 18669, 18705, 90738, 103759, 103965, ...

%e For example, T(3,1) = 1 because the determinant of the circulant starting with [0, 0, 1] is 1. For the same reason each row starts with 1.

%e T(3,2) = 8 = 020[4] (digits in base 4) = det(circulant([0, 2, 0])).

%e T(3,5) = 35 = 203[4] = det(circulant([2, 0, 3])).

%o (PARI) for(n=1,7,for(k=1,(n+1)^n-1,d=Vec(digits(k,n+1),-n);abs(matdet(matrix(n,n,i,j,d[(j-i)%n+1])))==k&&print1(k",")))

%Y Cf. A303261, A303260, A219324, A219325, A219326, A219327.

%K nonn,base,tabf

%O 1,4

%A _M. F. Hasler_, Apr 23 2018