A062186 -id:A062186 - cp's OEIS frontend

A062188 a(n+1) = a(n) + a(floor(n/2)), with a(0)=0, a(1)=1.

0, 1, 1, 2, 3, 4, 5, 7, 9, 12, 15, 19, 23, 28, 33, 40, 47, 56, 65, 77, 89, 104, 119, 138, 157, 180, 203, 231, 259, 292, 325, 365, 405, 452, 499, 555, 611, 676, 741, 818, 895, 984, 1073, 1177, 1281, 1400, 1519, 1657, 1795, 1952, 2109, 2289, 2469, 2672, 2875, 3106

Offset: 0

Henry Bottomley, Jun 13 2001

nonn

			a(6) = a(5)+a(2) = 4+1 = 5.
a(7) = a(6)+a(3) = 5+2 = 7.

Ivan Neretin, Table of n, a(n) for n = 0..10000

Cf. A033485, A062186, A062187.

[n le 2 select n-1 else  Self(n-1)+Self(Floor(n/2)): n in [1..60]]; // Vincenzo Librandi, Mar 03 2016

Join[{0}, Nest[Append[#, #[[-1]] + #[[Quotient[Length@#, 2]]]] &, {1, 1}, 53]] (* Ivan Neretin, Mar 03 2016 *)

from itertools import islice
from collections import deque
def A062188_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
A062188_list = list(islice(A062188_gen(),40)) # Chai Wah Wu, Jun 08 2022

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

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

Original entry on oeis.org

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

Henry Bottomley, Jun 13 2001

sign

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

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

Cf. A033485, A062186, A062188.

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

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

cp's OEIS Frontend

A062188 a(n+1) = a(n) + a(floor(n/2)), with a(0)=0, a(1)=1.

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