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A062186
a(n) = a(n-1) - a(floor(n/2)), with a(1)=1.
2
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
1,8
COMMENTS
Period of oscillations above and below the axis more than doubles at each cycle.
FORMULA
G.f.: A(x) satisfies: A(x) = (x - (1 + x)*A(x^2))/(1 - x). - Ilya Gutkovskiy, May 04 2019
EXAMPLE
a(14) = a(13) - a(7) = 5 - 1 = 4.
a(15) = a(14) - a(7) = 4 - 1 = 3.
PROG
(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
CROSSREFS
KEYWORD
sign
AUTHOR
Henry Bottomley, Jun 13 2001
STATUS
approved