A117449 - OEIS

%I #7 Jun 03 2021 02:10:04

%S 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,

%T -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,

%U -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

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

%H G. C. Greubel, <a href="/A117449/b117449.txt">Rows n = 0..50 of the triangle, flattened</a>

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

%e Triangle begins as:

%e   1;

%e   0,  1;

%e   0, -1,  1;

%e   0, -1,  1, 1;

%e   0,  1, -1, 0,  1;

%e   0, -2,  2, 0, -1,  1;

%e   0, -1,  1, 0, -1,  1, 1;

%e   0,  1, -1, 0,  1, -1, 0,  1;

%e   0, -2,  2, 0, -2,  2, 0, -1,  1;

%e   0, -1,  1, 0, -1,  1, 0, -1,  1, 1;

%e   0,  1, -1, 0,  1, -1, 0,  1, -1, 0, 1;

%t A117446[n_, k_]:= If[k<=n, Binomial[JacobiSymbol[k-1, 3], n-k], 0];

%t m = With[{nmax = 20}, Table[A117446[i, j], {i,nmax}, {j,nmax}]];

%t Table[Inverse[m][[n, k]], {n, 15}, {k, n}]//Flatten (* _G. C. Greubel_, Jun 03 2021 *)

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

%K sign,tabl

%O 0,17

%A _Paul Barry_, Mar 16 2006