%I #17 Dec 22 2021 14:16:49

%S 1,0,2,2,0,2,4,0,4,0,4,4,4,2,2,0,8,0,12,0,12,10,8,10,10,8,8,10,32,0,

%T 32,0,32,0,32,0,30,28,30,28,26,30,30,26,28,0,104,0,100,0,104,0,104,0,

%U 100,94,92,94,94,92,92,94,94,92,92,94,344,0,344,0,336,0,344,0,344,0,336,0

%N Triangle T(n,k), n >= 1, 0 <= k <= n-1, read by rows, where T(n,k) is the number of solutions to 1 +- 2 +- 3 +- ... +- n == k (mod n).

%C a(n) is even for n > 1.

%e Triangle begins:

%e 1;

%e 0, 2;

%e 2, 0, 2;

%e 4, 0, 4, 0;

%e 4, 4, 4, 2, 2;

%e 0, 8, 0, 12, 0, 12;

%e 10, 8, 10, 10, 8, 8, 10;

%e 32, 0, 32, 0, 32, 0, 32, 0;

%e 30, 28, 30, 28, 26, 30, 30, 26, 28;

%e 0, 104, 0, 100, 0, 104, 0, 104, 0, 100;

%o (Ruby)

%o def A(n)

%o ary = Array.new(n, 0)

%o [1, -1].repeated_permutation(n - 1){|i|

%o ary[(2..n).inject(1){|s, j| s + i[j - 2] * j} % n] += 1

%o }

%o ary

%o end

%o def A350272(n)

%o (1..n).map{|i| A(i)}.flatten

%o end

%o p A350272(10)

%Y Row sums give A131577.

%Y Column 0 gives A300190.

%K nonn,tabl

%O 1,3

%A _Seiichi Manyama_, Dec 22 2021