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A117449
Inverse of a number triangle related to L(n/3), where L(j/p) is the Legendre symbol of j and p.
2
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
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
KEYWORD
sign,tabl
AUTHOR
Paul Barry, Mar 16 2006
STATUS
approved