A111143 Number of different ways of drawing chords in a circle of numbers from 1 to n such that the sums of the numbers on the two sides of the chord are equal.

1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 0, 1, 2, 2, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 2, 0, 0, 1, 1, 0, 2, 2, 1, 0, 0, 1, 2, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 3, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 1, 2, 4, 3, 2, 1, 0, 0, 3, 1, 0, 0, 1, 2, 0, 0, 2, 1, 0, 3, 2, 1, 0, 0, 1, 2, 1, 0, 1, 4, 0, 0, 2, 1, 4, 0, 1, 3, 0

Offset

2,8

Links

Alois P. Heinz, Table of n, a(n) for n = 2..10000

Example

a(5) = 1 because in a circle with the numbers from 1 to 5 we can put a chord from 1 and 4 and the sum of both sides is the same.
a(9) = 2 as in a circle with the numbers from 1 to 9 we can put a chord in two ways, one from 2 to 7 and another from 6 to 9.

Maple

a:= proc(n) local c, i, j, u, v;
      c, i, j, u, v:= 0, 1, 2, 0, n*(n+1)/2-3;
      while j<=n do
         c:= c + `if`(u=v, 1, 0);
         if u>v then u, v:= u-i-1, v+i; i:=i+1
                else u, v:= u+j, v-j-1; j:=j+1
         fi;
      od; c
    end:
seq(a(n), n=2..100);  # Alois P. Heinz, Sep 12 2011

Mathematica

a[n_] := Module[{c = 0, i = 1, j = 2, u = 0, v = n(n+1)/2 - 3}, While[j <= n, c += If[u == v, 1, 0]; If[u > v, {u, v} = {u - i - 1, v + i}; i++,  {u, v} = {u + j, v - j - 1}; j++]]; c];
a /@ Range[2, 100] (* Jean-François Alcover, Nov 18 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A137867 A324734 A359902 * A356969 A342955 A004197

Adjacent sequences: A111140 A111141 A111142 * A111144 A111145 A111146

Keyword

easy,nonn

Author

Joao B. Oliveira (oliveira(AT)inf.pucrs.br), Oct 18 2005

Status

approved