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A300307 Number of solutions to 1 +- 3 +- 6 +- ... +- n*(n+1)/2 == 0 mod n. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A195395 A296805 A084247 * A286606 A266587 A070692

Adjacent sequences:  A300304 A300305 A300306 * A300308 A300309 A300310

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 02 2018

STATUS

approved

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)