%I #20 Nov 07 2024 08:32:37

%S 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,

%T 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,

%U 32,10,8,8,0,0,4,12,0,-2,10,6,0,0,4,18,0,42

%N Row sums of triangle A215200.

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

%H Robert Israel, <a href="/A215283/b215283.txt">Table of n, a(n) for n = 1..10000</a>

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

%p f:= n -> add(numtheory:-jacobi(n-k,k),k=1..n); # _Robert Israel_, Mar 11 2018

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

%o (Sage)

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

%o [sum(A215200_row(n)) for n in (1..81)]

%o (PARI) a(n) = sum(k = 1, n, kronecker(n-k, k)); \\ _Amiram Eldar_, Nov 07 2024

%Y Cf. A000010, A054521, A215200, A215284.

%K sign,look

%O 1,3

%A _Peter Luschny_, Aug 07 2012