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

1,4

Links

Table of n, a(n) for n=1..51.

Example

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])).

Prog

(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", ")))

Crossrefs

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

Sequence in context: A139753 A046874 A316416 * A225364 A304922 A181900

Adjacent sequences: A303259 A303260 A303261 * A303263 A303264 A303265

Keyword

nonn,base,tabf

Author

M. F. Hasler, Apr 23 2018

Status

approved