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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 MATHEMATICA b[n_, i_, m_] := b[n, i, m] = If[i == 0, If[n == 0, 1, 0], Sum[b[Mod[n + j, m], i - 1, m], {j, {i^3, m - i^3}}]]; a[n_] := b[0, n - 1, n]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Mar 19 2022, after Alois P. Heinz *) 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 A358641 A057277 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 June 8 18:04 EDT 2023. Contains 363165 sequences. (Running on oeis4.)