A347027 a(1) = 1; a(n) = a(n-1) + 2 * a(floor(n/2)).

1, 3, 5, 11, 17, 27, 37, 59, 81, 115, 149, 203, 257, 331, 405, 523, 641, 803, 965, 1195, 1425, 1723, 2021, 2427, 2833, 3347, 3861, 4523, 5185, 5995, 6805, 7851, 8897, 10179, 11461, 13067, 14673, 16603, 18533, 20923, 23313, 26163, 29013, 32459, 35905, 39947, 43989

Offset: 1

Author

Ilya Gutkovskiy, Aug 11 2021

Keywords

• nonn

Crossrefs

Cf. A033485, A033489, A058039.

Partial sums of A039722.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = a[n - 1] + 2 a[Floor[n/2]]; Table[a[n], {n, 1, 47}]
nmax = 47; A[] = 0; Do[A[x] = (x + 2 (1 + x) A[x^2])/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

Python

from collections import deque
from itertools import islice
def A347027_gen(): # generator of terms
    aqueue, f, b, a = deque([3]), True, 1, 3
    yield from (1, 3)
    while True:
        a += 2*b
        yield a
        aqueue.append(a)
        if f: b = aqueue.popleft()
        f = not f
A347027_list = list(islice(A347027_gen(),40)) # Chai Wah Wu, Jun 08 2022

Formula

G.f. A(x) satisfies: A(x) = (x + 2 * (1 + x) * A(x^2)) / (1 - x).

a(n) = 1 + 2 * Sum_{k=2..n} a(floor(k/2)).