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A306595 Determinant of the circulant matrix whose first column corresponds to the binary digits of n. 2
0, 1, 1, 0, 1, 2, 2, 0, 1, 0, 0, 3, 0, -3, 3, 0, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 0, 1, 0, 4, 0, 0, -9, 9, 0, 4, 9, 0, 8, 9, 0, 8, 5, 0, 0, 9, 0, -9, -8, 0, -5, 0, 0, 8, 5, 0, -5, 5, 0, 1, 2, 2, 3, 2, 24, 24, 4, 2, 3, 3, 32, 3, 4, 32, 5, 2, 24, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

This sequence is the binary variant of A177894.

From Robert Israel, Mar 05 2019: (Start)

a(n) is divisible by A000120(n).

If A070939(n) is even then n is divisible by A000120(n)*A065359(n). (End)

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

Wikipedia, Circulant matrix

Index entries for sequences related to binary expansion of n

FORMULA

a(A121016(n)) = 0 for any n > 0.

a(2^k) = 1 for any k >= 0.

a(A219325(n)) = A219325(n) for any n > 0.

EXAMPLE

For n = 13:

- the binary representation of 13 is "1101",

- the corresponding circulant matrix is:

    [1 1 0 1]

    [1 1 1 0]

    [0 1 1 1]

    [1 0 1 1]

- its determinant is -3,

- hence a(13) = -3.

MAPLE

a:= n-> `if`(n=1, 1, (l-> LinearAlgebra[Determinant](Matrix(nops(l),

       shape=Circulant[l[-i]$i=1..nops(l)])))(convert(n, base, 2))):

seq(a(n), n=0..100);  # Alois P. Heinz, Mar 05 2019

PROG

(PARI) a(n) = my (d=if (n, binary(n), [0])); my (m=matrix(#d, #d, i, j, d[1+(i-j)%#d])); return (matdet(m))

CROSSREFS

Cf. A000120, A065359,  A070939, A121016, A177894, A219325, A306714.

Sequence in context: A248211 A049502 A242284 * A332996 A292592 A292274

Adjacent sequences:  A306592 A306593 A306594 * A306596 A306597 A306598

KEYWORD

sign,base,look

AUTHOR

Rémy Sigrist, Feb 27 2019

STATUS

approved

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Last modified April 1 03:22 EDT 2020. Contains 333155 sequences. (Running on oeis4.)