A303262 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.
1, 1, 1, 8, 9, 28, 35, 1, 65, 80, 91, 1, 44, 99, 550, 854, 1936, 2761, 3421, 3732, 4043, 4354, 1, 63, 65, 2527, 3311, 3969, 4095, 13545, 13889, 1, 128, 129, 145, 6066, 16384, 16385, 16512, 16513, 16641, 18560, 18577, 18669, 18705, 90738, 103759, 103965, 109220, 120142, 121920
Offset: 1
Examples
The table starts (n=1) 1, (n=2) 1, (n=3) 1, 8, 9, 28, 35, (n=4) 1, 65, 80, 91, (n=5) 1, 44, 99, 550, 854, 1936, 2761, 3421, 3732, 4043, 4354, (n=6) 1, 63, 65, 2527, 3311, 3969, 4095, 13545, 13889, (n=7) 1, 128, 129, 145, 6066, 16384, 16385, 16512, 16513, 16641, 18560, 18577, 18669, 18705, 90738, 103759, 103965, ... 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. T(3,2) = 8 = 020[4] (digits in base 4) = det(circulant([0, 2, 0])). T(3,5) = 35 = 203[4] = det(circulant([2, 0, 3])).
Programs
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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",")))