A215200 Triangle read by rows, Kronecker symbol (n-k|k) for n >= 1, 1 <= k <= n.

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

Offset

1,1

Comments

Signed version of A054521.

References

Henri Cohen: A Course in Computational Algebraic Number Theory, p. 29.

Links

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

Eric Weisstein's World of Mathematics, Kronecker Symbol.

Example

Triangle begins:
  1,
  1,  0,
  1,  1,  0,
  1,  0,  1, 0,
  1, -1, -1, 1,  0,
  1,  0,  0, 0,  1, 0,
  1, -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,
From Jianing Song, Dec 26 2018: (Start)
This sequence can also be arranged into a square array T(n,k) = Kronecker symbol(n|k) with n >= 0, k >= 1, read by antidiagonals:
  1  0  0  0  0  0  0 ... ((0|k) = A000007(k+1))
  1  1  1  1  1  1  1 ... ((1|k) = A000012)
  1  0 -1  0 -1  0 -1 ... ((2|k) = A091337)
  1 -1  0  1 -1  0 -1 ... ((3|k) = A091338)
  1  0  1  0  1  0  1 ... ((4|k) = A000035)
  1 -1 -1  1  0  1 -1 ... ((5|k) = A080891)
  1  0  0  0  1  0 -1 ... ((6|k) = A322796)
  1  1  1  1 -1  1  0 ... ((7|k) = A089509)
  ... (End)

Maple

A215200_row := n -> seq(numtheory[jacobi](n-k, k), k=1..n);
for n from 1 to 13 do A215200_row(n) od;

Mathematica

Column[Table[KroneckerSymbol[n - k, k], {n, 10}, {k, n}], Center] (* Alonso del Arte, Aug 06 2012 *)

Prog

(Sage)
def A215200_row(n): return [kronecker_symbol(n-k, k) for k in (1..n)]
for n in (1..13): print(A215200_row(n))
(PARI) T(n, k) = kronecker(n-k, k);
tabl(nn) = for(n=1, nn, for(k=1, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Apr 24 2018
(Magma) /* As triangle */ [[KroneckerSymbol(n-k, k):  k in [1..n]]: n in [1..21]]; // Vincenzo Librandi, Apr 24 2018

Crossrefs

Rows of square array include: A000012, A091337, A091338, A000035, A080891, A322796, A089509.

Cf. A054521, A215283, A215284, A215285.

Sequence in context: A168030 A128431 A290452 * A054521 A349221 A338354

Adjacent sequences: A215197 A215198 A215199 * A215201 A215202 A215203

Keyword

sign,tabl

Author

Peter Luschny, Aug 05 2012

Status

approved