A300307 Number of solutions to 1 +- 3 +- 6 +- ... +- n*(n+1)/2 == 0 mod n.

1, 2, 0, 4, 4, 16, 12, 32, 20, 112, 88, 384, 308, 1264, 1056, 4096, 3852, 15120, 13820, 52608, 49824, 190848, 182356, 704512, 671540, 2582128, 2475220, 9615744, 9256428, 35868672, 34636840, 134217728, 130021392, 505292976, 491156304, 1909836416, 1857282536

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..2^11

Formula

a(2^n) = 2^A000325(n) for n>0 (conjectured).

Example

Solutions for n = 7:
------------------------------
1 +3 +6 +10 +15 +21 +28 =  84.
1 +3 +6 +10 +15 +21 -28 =  28.
1 +3 +6 +10 +15 -21 +28 =  42.
1 +3 +6 +10 +15 -21 -28 = -14.
1 +3 -6 +10 -15 +21 +28 =  42.
1 +3 -6 +10 -15 +21 -28 = -14.
1 +3 -6 +10 -15 -21 +28 =   0.
1 +3 -6 +10 -15 -21 -28 = -56.
1 -3 +6 -10 -15 +21 +28 =  28.
1 -3 +6 -10 -15 +21 -28 = -28.
1 -3 +6 -10 -15 -21 +28 = -14.
1 -3 +6 -10 -15 -21 -28 = -70.

Prog

(Ruby)
def A(n)
  ary = [1] + Array.new(n - 1, 0)
  (1..n).each{|i|
    it = i * (i + 1)
    a = ary.clone
    (0..n - 1).each{|j| a[(j + it) % n] += ary[j]}
    ary = a
  }
  ary[(n * (n + 1) * (n + 2) / 6) % n] / 2
end
def A300307(n)
  (1..n).map{|i| A(i)}
end
p A300307(100)

Crossrefs

Cf. A000079, A000217, A000325, A058498, A300190, A300218.

Sequence in context: A296805 A336974 A084247 * A286606 A266587 A070692

Adjacent sequences: A300304 A300305 A300306 * A300308 A300309 A300310

Keyword

nonn

Author

Seiichi Manyama, Mar 02 2018

Status

approved