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Square array read by antidiagonals: T(n,k) = Kronecker symbol (-n/k), n >= 1, k >= 1.
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%I #17 Apr 21 2022 21:56:16

%S 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,

%T 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,

%U 1,0,0,0,-1,1,-1,-1,1,-1,-1,1,-1,1,1,1,-1

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

%C 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.

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KroneckerSymbol.html">Kronecker Symbol</a>.

%e Table begins

%e 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, ... ((-1/k) = A034947)

%e 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, ... ((-2/k) = A188510)

%e 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, ... ((-3/k) = A102283)

%e 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, ... ((-4/k) = A101455)

%e 1, -1, 1, 1, 0, -1, 1, -1, 1, 0, ... ((-5/k) = A226162)

%e 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, ... ((-6/k) = A109017)

%e 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, ... ((-7/k) = A175629)

%e 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, ... ((-8/k) = A188510)

%e ...

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

%Y Cf. A215200.

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

%K sign,tabl

%O 1,1

%A _Jianing Song_, Jan 12 2019