>>747

 a[1] = -1/2,
 a[n] = 2a[n-1] + (n/2)^2 + n, (n:偶数)
    = (1/2)a[n-1] - (n+1)/4, (n:奇数)

 a[n] = (1/48)(n-3)(n+1)(n+5)  (n:奇数)
    = (1/24)n(n+2)(n+4)    (n:偶数)

 n=4m+1 のとき a[n] = (整数)+1/2,
 その他のとき a[n] = 偶数。