A350272 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).

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, 32, 0, 32, 0, 32, 0, 30, 28, 30, 28, 26, 30, 30, 26, 28, 0, 104, 0, 100, 0, 104, 0, 104, 0, 100, 94, 92, 94, 94, 92, 92, 94, 94, 92, 92, 94, 344, 0, 344, 0, 336, 0, 344, 0, 344, 0, 336, 0

Offset: 1

Author

Seiichi Manyama, Dec 22 2021

Keywords

• nonn
• tabl

Comments

a(n) is even for n > 1.

Examples

			Triangle begins:
   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, 32,   0, 32,   0, 32,   0;
  30,  28, 30,  28, 26,  30, 30,  26, 28;
   0, 104,  0, 100,  0, 104,  0, 104,  0, 100;
		

Crossrefs

Row sums give A131577.

Column 0 gives A300190.

Programs

Ruby

def A(n)
  ary = Array.new(n, 0)
  [1, -1].repeated_permutation(n - 1){|i|
    ary[(2..n).inject(1){|s, j| s + i[j - 2] * j} % n] += 1
  }
  ary
end
def A350272(n)
  (1..n).map{|i| A(i)}.flatten
end
p A350272(10)