The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A300190 Number of solutions to 1 +- 2 +- 3 +- ... +- n == 0 (mod n). 9
 1, 0, 2, 4, 4, 0, 10, 32, 30, 0, 94, 344, 316, 0, 1096, 4096, 3856, 0, 13798, 52432, 49940, 0, 182362, 699072, 671092, 0, 2485534, 9586984, 9256396, 0, 34636834, 134217728, 130150588, 0, 490853416, 1908874584, 1857283156, 0, 7048151672, 27487790720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Apparently a(2*n + 1) = A053656(2*n + 1) for n >= 0. - Georg Fischer, Mar 26 2019 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..3334 (terms 1..1000 from Alois P. Heinz) FORMULA a(4*n+1) = A000016(n), a(4*n+2) = 0, a(4*n+3) = A000016(n), a(4*n+4) = 2 * A000016(n) for n > 0. a(2^n) = 2^A000325(n) for n > 1. EXAMPLE Solutions for n = 7: -------------------------- 1 +2 +3 +4 +5 +6 +7 = 28. 1 +2 +3 +4 +5 +6 -7 = 14. 1 +2 -3 +4 -5 -6 +7 = 0. 1 +2 -3 +4 -5 -6 -7 = -14. 1 +2 -3 -4 +5 +6 +7 = 14. 1 +2 -3 -4 +5 +6 -7 = 0. 1 -2 +3 +4 -5 +6 +7 = 14. 1 -2 +3 +4 -5 +6 -7 = 0. 1 -2 -3 -4 -5 +6 +7 = 0. 1 -2 -3 -4 -5 +6 -7 = -14. 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, m-i])) 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, m - i}}]]; a[n_] := b[0, n - 1, n]; Array[a, 60] (* Jean-François Alcover, Apr 29 2020, after Alois P. Heinz *) PROG (Ruby) def A(n) ary = [1] + Array.new(n - 1, 0) (1..n).each{|i| i1 = 2 * i a = ary.clone (0..n - 1).each{|j| a[(j + i1) % n] += ary[j]} ary = a } ary[(n * (n + 1) / 2) % n] / 2 end def A300190(n) (1..n).map{|i| A(i)} end p A300190(100) CROSSREFS Number of solutions to 1 +- 2^k +- 3^k +- ... +- n^k == 0 (mod n): this sequence (k=1), A300268 (k=2), A300269 (k=3). Cf. A000016, A026119, A053656, A058377, A063776, A300307, A300328. Cf. A016825 (4n+2). Sequence in context: A118434 A090132 A199051 * A099211 A261761 A300269 Adjacent sequences: A300187 A300188 A300189 * A300191 A300192 A300193 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 28 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 4 03:55 EDT 2023. Contains 363118 sequences. (Running on oeis4.)