A215200 Triangle read by rows, Kronecker symbol (n-k|k) for n >= 1, 1 <= k <= n.
1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, -1, -1, 1, 0, 1, 0, 0, 0, 1, 0, 1, -1, 1, 1, -1, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0
Offset: 1
Examples
Triangle begins: 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, -1, -1, 1, 0, 1, 0, 0, 0, 1, 0, 1, -1, 1, 1, -1, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, From _Jianing Song_, Dec 26 2018: (Start) This sequence can also be arranged into a square array T(n,k) = Kronecker symbol(n|k) with n >= 0, k >= 1, read by antidiagonals: 1 0 0 0 0 0 0 ... ((0|k) = A000007(k+1)) 1 1 1 1 1 1 1 ... ((1|k) = A000012) 1 0 -1 0 -1 0 -1 ... ((2|k) = A091337) 1 -1 0 1 -1 0 -1 ... ((3|k) = A091338) 1 0 1 0 1 0 1 ... ((4|k) = A000035) 1 -1 -1 1 0 1 -1 ... ((5|k) = A080891) 1 0 0 0 1 0 -1 ... ((6|k) = A322796) 1 1 1 1 -1 1 0 ... ((7|k) = A089509) ... (End)
References
- Henri Cohen: A Course in Computational Algebraic Number Theory, p. 29.
Links
- G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened
- Eric Weisstein's World of Mathematics, Kronecker Symbol.
Crossrefs
Programs
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Magma
/* As triangle */ [[KroneckerSymbol(n-k, k): k in [1..n]]: n in [1..21]]; // Vincenzo Librandi, Apr 24 2018
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Maple
A215200_row := n -> seq(numtheory[jacobi](n-k,k),k=1..n); for n from 1 to 13 do A215200_row(n) od;
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Mathematica
Column[Table[KroneckerSymbol[n - k, k], {n, 10}, {k, n}], Center] (* Alonso del Arte, Aug 06 2012 *) -
PARI
T(n,k) = kronecker(n-k, k); tabl(nn) = for(n=1, nn, for(k=1, n, print1(T(n,k), ", ")); print); \\ Michel Marcus, Apr 24 2018
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Sage
def A215200_row(n): return [kronecker_symbol(n-k,k) for k in (1..n)] for n in (1..13): print(A215200_row(n))
Comments