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

1,3

Comments

a(n) is even for n > 1.

Links

Table of n, a(n) for n=1..78.

Example

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;

Prog

(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)

Crossrefs

Row sums give A131577.

Column 0 gives A300190.

Sequence in context: A102706 A105673 A259761 * A171933 A074823 A226177

Adjacent sequences: A350269 A350270 A350271 * A350273 A350274 A350275

Keyword

nonn,tabl

Author

Seiichi Manyama, Dec 22 2021

Status

approved