STATUS
proposed
approved
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Revision History for A347027
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
editing
proposed
CROSSREFS
Partial sums of A039722.
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
PROG
(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
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
NAME
allocated for Ilya Gutkovskiy
a(1) = 1; a(n) = a(n-1) + 2 * a(floor(n/2)).
DATA
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
1,2
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)).
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
KEYWORD
allocated
nonn
AUTHOR
Ilya Gutkovskiy, Aug 11 2021
STATUS
approved
editing