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

Author

Seiichi Manyama, Feb 28 2018

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A063776, A156700, A300190.

Programs

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 *)