|
|
A215200
|
|
Triangle read by rows, Kronecker symbol (n-k|k) for n >= 1, 1 <= k <= n.
|
|
9
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
REFERENCES
|
Henri Cohen: A Course in Computational Algebraic Number Theory, p. 29.
|
|
LINKS
|
|
|
EXAMPLE
|
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,
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)
|
|
MAPLE
|
A215200_row := n -> seq(numtheory[jacobi](n-k, k), k=1..n);
for n from 1 to 13 do A215200_row(n) od;
|
|
MATHEMATICA
|
Column[Table[KroneckerSymbol[n - k, k], {n, 10}, {k, n}], Center] (* Alonso del Arte, Aug 06 2012 *)
|
|
PROG
|
(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))
(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
(Magma) /* As triangle */ [[KroneckerSymbol(n-k, k): k in [1..n]]: n in [1..21]]; // Vincenzo Librandi, Apr 24 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|