A062186 a(n) = a(n-1) - a(floor(n/2)), with a(1)=1.

1, 0, -1, -1, -1, 0, 1, 2, 3, 4, 5, 5, 5, 4, 3, 1, -1, -4, -7, -11, -15, -20, -25, -30, -35, -40, -45, -49, -53, -56, -59, -60, -61, -60, -59, -55, -51, -44, -37, -26, -15, 0, 15, 35, 55, 80, 105, 135, 165, 200, 235, 275, 315, 360, 405, 454, 503, 556, 609, 665, 721, 780, 839, 899, 959, 1020, 1081, 1141, 1201, 1260

Offset: 1

Author

Henry Bottomley, Jun 13 2001

Keywords

• sign

Comments

Period of oscillations above and below the axis more than doubles at each cycle.

Examples

			a(14) = a(13) - a(7) = 5 - 1 = 4.
a(15) = a(14) - a(7) = 4 - 1 = 3.
		

Crossrefs

Cf. A033485, A062187, A062188.

Programs

Python

from itertools import islice
from collections import deque
def A062186_gen(): # generator of terms
    aqueue, f, b, a = deque([0]), True, 1, 0
    yield from (1,0)
    while True:
        a -= b
        yield a
        aqueue.append(a)
        if f: b = aqueue.popleft()
        f = not f
A062186_list = list(islice(A062186_gen(),40)) # Chai Wah Wu, Jun 08 2022

Formula

G.f.: A(x) satisfies: A(x) = (x - (1 + x)*A(x^2))/(1 - x). - Ilya Gutkovskiy, May 04 2019