A323378 Square array read by antidiagonals: T(n,k) = Kronecker symbol (-n/k), n >= 1, k >= 1.

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

Offset

1,1

Comments

If A215200 is arranged into a square array A215200(n,k) = kronecker symbol(n/k) with n >= 0, k >= 1, then this sequence gives the other half of the array.

Note that there is no such n such that the n-th row and the n-th column are the same.

Links

Paolo Xausa, Table of n, a(n) for n = 1..11325 (first 150 antidiagonals, flattened).

Eric Weisstein's World of Mathematics, Kronecker Symbol.

Example

Table begins
  1,  1, -1,  1,  1, -1, -1,  1,  1,  1, ... ((-1/k) = A034947)
  1,  0,  1,  0, -1,  0, -1,  0,  1,  0, ... ((-2/k) = A188510)
  1, -1,  0,  1, -1,  0,  1, -1,  0,  1, ... ((-3/k) = A102283)
  1,  0, -1,  0,  1,  0, -1,  0,  1,  0, ... ((-4/k) = A101455)
  1, -1,  1,  1,  0, -1,  1, -1,  1,  0, ... ((-5/k) = A226162)
  1,  0,  0,  0,  1,  0,  1,  0,  0,  0, ... ((-6/k) = A109017)
  1,  1, -1,  1, -1, -1,  0,  1,  1, -1, ... ((-7/k) = A175629)
  1,  0,  1,  0, -1,  0, -1,  0,  1,  0, ... ((-8/k) = A188510)
  ...

Mathematica

Table[KroneckerSymbol[k - n - 1, k], {n, 15}, {k, n}] (* Paolo Xausa, Sep 15 2025 *)

Prog

(PARI) T(n, k) = kronecker(-n, k)

Crossrefs

Cf. A215200.

The first rows are listed in A034947, A188510, A102283, A101455, A226162, A109017, A175629, A188510, ...

Sequence in context: A143200 A166282 A047999 * A054431 A164381 A106470

Adjacent sequences: A323375 A323376 A323377 * A323379 A323380 A323381

Keyword

sign,tabl

Author

Jianing Song, Jan 12 2019

Status

approved