A215283 Row sums of triangle A215200.

1, 1, 2, 2, 0, 2, 2, 0, 6, 2, 6, 0, 2, 4, 4, 8, 4, 0, 8, 0, 0, 2, 4, 0, 14, 6, 2, 0, -2, 4, 8, 0, 2, 4, 12, 12, 4, 6, 10, 0, 10, 4, 8, 0, 2, 4, 6, 0, 32, 2, 12, 0, 0, 2, 12, 0, 2, 2, 18, 0, 2, 8, 2, 32, 10, 8, 8, 0, 0, 4, 12, 0, -2, 10, 6, 0, 0, 4, 18, 0, 42

Offset: 1

Author

Peter Luschny, Aug 07 2012

Keywords

• sign
• look

Comments

The unsigned version of A215200 is A054521 which has as row sums the Euler totient function A000010.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A054521, A215200, A215284.

Programs

Maple

f:= n -> add(numtheory:-jacobi(n-k,k),k=1..n); # Robert Israel, Mar 11 2018

Mathematica

a[n_] := Sum[ KroneckerSymbol[n - k, k], {k, 1, n}]; Table[a[n], {n, 1, 81}] (* Jean-François Alcover, Jul 02 2013 *)

PARI

a(n) = sum(k = 1, n, kronecker(n-k, k)); \\ Amiram Eldar, Nov 07 2024

Sage

def A215200_row(n): return [kronecker_symbol(n-k, k) for k in (1..n)]
[sum(A215200_row(n)) for n in (1..81)]

Formula

a(n) = Sum_{k=1..n} (n-k | k) where (i | j) is the Kronecker symbol.