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

Author

Peter Luschny, Aug 05 2012

Keywords

• sign
• tabl

Comments

Signed version of A054521.

Examples

			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)
		

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.

Crossrefs

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

Cf. A054521, A215283, A215284, A215285.

Programs

Magma

/* As triangle */ [[KroneckerSymbol(n-k, k):  k in [1..n]]: n in [1..21]]; // Vincenzo Librandi, Apr 24 2018

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 *)

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

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))