A124895 Triangle read by rows, 1 <= k <= n: T(n,k) = mu(n^2 + k^2) with mu = A008683.

-1, -1, 0, 1, -1, 0, -1, 0, 0, 0, 1, -1, 1, -1, 0, -1, 0, 0, 0, -1, 0, 0, -1, 1, 1, 1, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 1, 0, -1, -1, 1, -1, -1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, -1, 1, 1, 1, 1, 1, -1, 0, -1, -1, -1, 0, -1, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 1, -1, 0, -1, 0, 0, 1, 0, 0, 0, 1, 0, 1, -1, 0

Offset: 1

Author

Reinhard Zumkeller, Nov 12 2006

Keywords

• sign
• tabl
• easy

Examples

			Triangle begins:
 -1
 -1,  0
  1, -1,  0
 -1,  0,  0,  0
  1, -1,  1, -1,  0
 -1,  0,  0,  0, -1, 0
  0, -1,  1,  1,  1, 1,  0
  1,  0, -1,  0, -1, 0, -1, 0
  1,  1,  0, -1,  1, 0, -1, 1,  0
 -1,  0, -1,  0,  0, 0, -1, 0, -1, 0
		

Crossrefs

Cf. A000007, A008683, A049532, A049533, A070216, A124897.

Programs

Mathematica

row[n_] := Table[MoebiusMu[n^2 + k^2], {k, 1, n}]; Array[row, 15] // Flatten (* Amiram Eldar, May 12 2025 *)

PARI

row(n) = vector(n, k, moebius(n^2 + k^2)); \\ Amiram Eldar, May 12 2025

Formula

T(n,k) = A008683(A070216(n,k)).

T(n,1) = A124897(1); T(A049533(n),1) <> 0; T(A049532(n),1) = 0.

T(n,n) = -A000007(n-1).

A124896(n) = Sum_{k=1..n} abs(T(n,k)), row sums of absolute values.