A062187 a(n+1) = a(n) - a(floor(n/2)), with a(0)=0, a(1)=1.

0, 1, 1, 0, -1, -2, -3, -3, -3, -2, -1, 1, 3, 6, 9, 12, 15, 18, 21, 23, 25, 26, 27, 26, 25, 22, 19, 13, 7, -2, -11, -23, -35, -50, -65, -83, -101, -122, -143, -166, -189, -214, -239, -265, -291, -318, -345, -371, -397, -422, -447, -469, -491, -510, -529, -542, -555, -562, -569, -567, -565, -554, -543, -520, -497, -462

Offset: 0

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(6) = a(5) - a(2) = -2 - 1 = -3.
a(7) = a(6) - a(3) = -3 - 0 = -3.
		

Crossrefs

Cf. A033485, A062186, A062188.

Programs

Python

from itertools import islice
from collections import deque
def A062187_gen(): # generator of terms
    aqueue, f, b, a = deque([1]), True, 0, 1
    yield from (0,1)
    while True:
        a -= b
        yield a
        aqueue.append(a)
        if f: b = aqueue.popleft()
        f = not f
A061287_list = list(islice(A062187_gen(),40)) # Chai Wah Wu, Jun 08 2022

Formula

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