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 A300268 Number of solutions to 1 +- 4 +- 9 +- ... +- n^2 == 0 (mod n). 3
 1, 0, 2, 4, 6, 0, 10, 48, 32, 0, 94, 344, 370, 0, 1268, 4608, 3856, 0, 13798, 55960, 50090, 0, 182362, 721952, 690496, 0, 2485592, 9586984, 9256746, 0, 34636834, 135335936, 130150588, 0, 493452348, 1908875264, 1857293524, 0, 7049188508, 27603824928 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..3334 (terms 1..1000 from Alois P. Heinz) EXAMPLE Solutions for n = 7: ------------------------------- 1 +4 +9 +16 +25 +36 +49 = 140. 1 +4 +9 +16 +25 +36 -49 = 42. 1 +4 +9 -16 -25 -36 +49 = -14. 1 +4 +9 -16 -25 -36 -49 = -112. 1 +4 -9 +16 -25 -36 +49 = 0. 1 +4 -9 +16 -25 -36 -49 = -98. 1 -4 +9 -16 +25 -36 +49 = 28. 1 -4 +9 -16 +25 -36 -49 = -70. 1 -4 -9 +16 +25 -36 +49 = 42. 1 -4 -9 +16 +25 -36 -49 = -56. 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^2, m-i^2])) 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^2, m - i^2}}]]; 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| i2 = 2 * i * i a = ary.clone (0..n - 1).each{|j| a[(j + i2) % n] += ary[j]} ary = a } ary[(n * (n + 1) * (2 * n + 1) / 6) % n] / 2 end def A300268(n) (1..n).map{|i| A(i)} end p A300268(100) (PARI) a(n) = my (v=vector(n, k, k==1)); for (i=2, n, v = vector(n, k, v[1 + (k-i^2)%n] + v[1 + (k+i^2)%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), this sequence (k=2), A300269 (k=3). Cf. A083527, A215573. Sequence in context: A013670 A121206 A062004 * A009285 A013082 A352639 Adjacent sequences: A300265 A300266 A300267 * A300269 A300270 A300271 KEYWORD nonn AUTHOR Seiichi Manyama, Mar 01 2018 STATUS approved

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Last modified September 30 02:05 EDT 2023. Contains 365781 sequences. (Running on oeis4.)