A117449 Inverse of a number triangle related to L(n/3), where L(j/p) is the Legendre symbol of j and p.

1, 0, 1, 0, -1, 1, 0, -1, 1, 1, 0, 1, -1, 0, 1, 0, -2, 2, 0, -1, 1, 0, -1, 1, 0, -1, 1, 1, 0, 1, -1, 0, 1, -1, 0, 1, 0, -2, 2, 0, -2, 2, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, 0, -2, 2, 0, -2, 2, 0, -2, 2, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 1

Offset

0,17

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Formula

Sum_{k=0..n} T(n, k) = A011655(n+1).

Example

Triangle begins as:
  1;
  0,  1;
  0, -1,  1;
  0, -1,  1, 1;
  0,  1, -1, 0,  1;
  0, -2,  2, 0, -1,  1;
  0, -1,  1, 0, -1,  1, 1;
  0,  1, -1, 0,  1, -1, 0,  1;
  0, -2,  2, 0, -2,  2, 0, -1,  1;
  0, -1,  1, 0, -1,  1, 0, -1,  1, 1;
  0,  1, -1, 0,  1, -1, 0,  1, -1, 0, 1;

Mathematica

A117446[n_, k_]:= If[k<=n, Binomial[JacobiSymbol[k-1, 3], n-k], 0];
m = With[{nmax = 20}, Table[A117446[i, j], {i, nmax}, {j, nmax}]];
Table[Inverse[m][[n, k]], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Jun 03 2021 *)

Crossrefs

Cf. A011655 (row sums), A117446 (inverse).

Sequence in context: A215573 A163537 A219946 * A004594 A124210 A287447

Adjacent sequences: A117446 A117447 A117448 * A117450 A117451 A117452

Keyword

sign,tabl

Author

Paul Barry, Mar 16 2006

Status

approved