A071768 Determinant of the n X n matrix whose element (i,j) equals |i-j| (Mod 3).

0, -1, 4, 9, -10, 4, 18, -19, 4, 27, -28, 4, 36, -37, 4, 45, -46, 4, 54, -55, 4, 63, -64, 4, 72, -73, 4, 81, -82, 4, 90, -91, 4, 99, -100, 4, 108, -109, 4, 117, -118, 4, 126, -127, 4, 135, -136, 4, 144, -145, 4, 153, -154, 4, 162, -163, 4, 171, -172, 4, 180, -181, 4, 189

Offset

1,3

Comments

(Mod 2) for n > 2 produces nothing but zeros.

Links

Table of n, a(n) for n=1..64.

Index entries for linear recurrences with constant coefficients, signature (-1,-1,1,1,1).

Formula

a(3k) = 4, a(3k+1) = 9*k, a(3k+2) = -9*k-1.

a(n) = -a(n-1)-a(n-2)+a(n-3)+a(n-4)+a(n-5). - Colin Barker, Sep 29 2014

G.f.: -x^2*(2*x+1)*(2*x^2+5*x-1) / ((x-1)*(x^2+x+1)^2). - Colin Barker, Sep 29 2014

Mathematica

Table[ Det[ Table[ Mod[ Abs[i - j], 3], {i, 1, n}, {j, 1, n}]], {n, 1, 65}]

Prog

(PARI) a(n) = matdet(matrix (n, n, i, j, abs(i-j) % 3)); \\ Michel Marcus, Sep 29 2014
(PARI) concat(0, Vec(-x^2*(2*x+1)*(2*x^2+5*x-1)/((x-1)*(x^2+x+1)^2) + O(x^100))) \\ Colin Barker, Sep 30 2014

Crossrefs

Cf. A071769 (with Mod 4).

Sequence in context: A156047 A171001 A088037 * A301478 A173297 A161913

Adjacent sequences: A071765 A071766 A071767 * A071769 A071770 A071771

Keyword

sign,easy

Author

Robert G. Wilson v, Jun 04 2002

Status

approved