A300218 Number of solutions to 1 +- 3 +- 5 +- ... +- (2*n-1) == 0 mod n.

1, 2, 2, 4, 4, 12, 10, 36, 30, 104, 94, 344, 316, 1172, 1096, 4132, 3856, 14572, 13798, 52432, 49940, 190652, 182362, 699416, 671092, 2581112, 2485534, 9586984, 9256396, 35791472, 34636834, 134221860, 130150588, 505290272, 490853416, 1908874584, 1857283156

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 200 terms from Seiichi Manyama)

Example

Solutions for n = 7:
----------------------------
1 +3 +5 +7 +9 +11 +13 =  49.
1 +3 +5 -7 +9 +11 +13 =  35.
1 +3 -5 +7 -9 +11 +13 =  21.
1 +3 -5 -7 -9 +11 +13 =   7.
1 -3 +5 +7 +9 -11 +13 =  21.
1 -3 +5 -7 +9 -11 +13 =   7.
1 -3 -5 +7 +9 +11 -13 =   7.
1 -3 -5 +7 -9 -11 +13 =  -7.
1 -3 -5 -7 +9 +11 -13 =  -7.
1 -3 -5 -7 -9 -11 +13 = -21.

Maple

b:= proc(n, i, m) option remember; `if`(i<1, `if`(n=0, 1, 0),
      add(b(irem(n+j, m), i-2, m), j=[i, m-i]))
    end:
a:= n-> b(n-1, 2*n-3, n):
seq(a(n), n=1..40);  # Alois P. Heinz, Mar 01 2018

Mathematica

Table[With[{s = Range[1, (2 n - 1), 2]}, Count[Map[Total[s #] &, Take[Tuples[{-1, 1}, Length@ s], -2^(n - 1)]], _?(Divisible[#, n] &)]], {n, 22}] (* Michael De Vlieger, Mar 01 2018 *)

Crossrefs

Cf. A063776, A156700, A300190.

Sequence in context: A218147 A226978 A243331 * A138317 A103659 A069947

Adjacent sequences: A300215 A300216 A300217 * A300219 A300220 A300221

Keyword

nonn

Author

Seiichi Manyama, Feb 28 2018

Status

approved