A110242 A Jacobi triangle.

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

Offset

0,1

Links

Table of n, a(n) for n=0..90.

Formula

T(n, k) = if(k<=n, Jacobi(n, 2n-2k+1), 0).

Example

Rows begin
1;
1,1;
-1,-1,1;
-1,-1,0,1;
1,1,1,1,1;
1,1,-1,0,-1,1;

Maple

A110242 := proc(n, k)
    if k<0 or k> n then
        0;
    else
        numtheory[jacobi](n, 2*n-2*k+1) ;
    end if;
end proc: # R. J. Mathar, Feb 20 2015

Mathematica

T[n_, k_] := JacobiSymbol[n, 2n - 2k + 1];
Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Mar 29 2020 *)

Crossrefs

Row sums are A110243. Diagonal sums are A110244. Inverse is A110245.

Sequence in context: A353628 A359551 A353458 * A356315 A273592 A279693

Adjacent sequences: A110239 A110240 A110241 * A110243 A110244 A110245

Keyword

easy,sign,tabl

Author

Paul Barry, Jul 17 2005

Status

approved