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A300269 Number of solutions to 1 +- 8 +- 27 +- ... +- n^3 == 0 mod n. 3
1, 0, 2, 4, 4, 0, 20, 48, 80, 0, 94, 344, 424, 0, 1096, 4864, 3856, 0, 16444, 52432, 65248, 0, 182362, 720928, 671104, 0, 4152320, 11156656, 9256396, 0, 34636834, 135397376, 130150588, 0, 533834992, 2773200896, 1857304312, 0, 7065319328, 27541477824, 26817356776 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

EXAMPLE

Solutions for n = 7:

-----------------------------------

1 +8 +27 +64 +125 +216 +343 =  784.

1 +8 +27 +64 +125 +216 -343 =   98.

1 +8 +27 -64 +125 -216 +343 =  224.

1 +8 +27 -64 +125 -216 -343 = -462.

1 +8 +27 -64 -125 +216 +343 =  406.

1 +8 +27 -64 -125 +216 -343 = -280.

1 +8 -27 -64 +125 +216 +343 =  602.

1 +8 -27 -64 +125 +216 -343 =  -84.

1 -8 +27 +64 +125 -216 +343 =  336.

1 -8 +27 +64 +125 -216 -343 = -350.

1 -8 +27 +64 -125 +216 +343 =  518.

1 -8 +27 +64 -125 +216 -343 = -168.

1 -8 +27 -64 -125 -216 +343 =  -42.

1 -8 +27 -64 -125 -216 -343 = -728.

1 -8 -27 +64 +125 +216 +343 =  714.

1 -8 -27 +64 +125 +216 -343 =   28.

1 -8 -27 -64 +125 -216 +343 =  154.

1 -8 -27 -64 +125 -216 -343 = -532.

1 -8 -27 -64 -125 +216 +343 =  336.

1 -8 -27 -64 -125 +216 -343 = -350.

MAPLE

b:= proc(n, i, m) option remember; `if`(i=0, `if`(n=0, 1, 0),

      add(b(irem(n+j, m), i-1, m), j=[i^3, m-i^3]))

    end:

a:= n-> b(0, n-1, n):

seq(a(n), n=1..60);  # Alois P. Heinz, Mar 01 2018

PROG

(Ruby)

def A(n)

  ary = [1] + Array.new(n - 1, 0)

  (1..n).each{|i|

    i3 = 2 * i * i * i

    a = ary.clone

    (0..n - 1).each{|j| a[(j + i3) % n] += ary[j]}

    ary = a

  }

  ary[((n * (n + 1)) ** 2 / 4) % n] / 2

end

def A300269(n)

  (1..n).map{|i| A(i)}

end

p A300269(100)

(PARI) a(n) = my (v=vector(n, k, k==1)); for (i=2, n, v = vector(n, k, v[1 + (k-i^3)%n] + v[1 + (k+i^3)%n])); v[1] \\ Rémy Sigrist, Mar 01 2018

CROSSREFS

Number of solutions to 1 +- 2^k +- 3^k +- ... +- n^k == 0 mod n: A300190 (k=1), A300268 (k=2), this sequence (k=3).

Cf. A113263, A195938.

Sequence in context: A300190 A099211 A261761 * A094225 A057277 A258712

Adjacent sequences:  A300266 A300267 A300268 * A300270 A300271 A300272

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 01 2018

EXTENSIONS

More terms from Alois P. Heinz, Mar 01 2018

STATUS

approved

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Last modified February 16 20:45 EST 2019. Contains 320189 sequences. (Running on oeis4.)