160522(3)

Ruby

Π(1 - q^n)(2)

オイラーの五角数定理を使うと高速に求まる。

オンライン整数列大辞典の
A010815（http://oeis.org/A010815/list）
と比較し、答え合わせしてみる。

def p0(n)
  (3 * n * n - n) / 2
end

def p1(n)
  (3 * n * n + n) / 2
end

def A010815(n)
  ary = Array.new(n + 1, 0)
  ary[0] = 1
  i = 1
  j = p0(i)
  while j <= n
    ary[j] = (-1) ** i
    i += 1
    j = p0(i)
  end
  i = 1
  j = p1(i)
  while j <= n
    ary[j] = (-1) ** i
    i += 1
    j = p1(i)
  end
  ary
end
ary = A010815(92)

# OEIS A010815のデータ
ary0 =
[1,-1,-1,0,0,1,0,1,0,0,0,0,-1,0,0,-1,0,0,0,0,0,0,
 1,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,
 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
 -1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]
# 一致の確認
p ary == ary0