A178855 Partial sums of A033485.

1, 3, 6, 11, 18, 28, 41, 59, 82, 112, 149, 196, 253, 323, 406, 507, 626, 768, 933, 1128, 1353, 1615, 1914, 2260, 2653, 3103, 3610, 4187, 4834, 5564, 6377, 7291, 8306, 9440, 10693, 12088, 13625, 15327, 17194, 19256, 21513, 23995, 26702, 29671, 32902, 36432

Offset: 1

Author

Philippe Deléham, Jun 19 2010

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000123, A033485.

Programs

Maple

b:= proc(n) option remember;
      `if`(n<2, n, b(n-1)+b(iquo(n, 2)))
    end:
a:= n-> (b(2*n+1)-1)/2:
seq(a(n), n=1..60);  # Alois P. Heinz, Feb 17 2022

Python

from itertools import islice
from collections import deque
def A178855_gen(): # generator of terms
    aqueue, f, b, a = deque([2]), True, 1, 2
    while True:
        a += b
        aqueue.append(a)
        if f:
            yield (a-1)//2
            b = aqueue.popleft()
        f = not f
A178885_list = list(islice(A178855_gen(),40)) # Chai Wah Wu, Jun 08 2022

Formula

a(n) = (A033485(2n+1)-1)/2.

Extensions

a(40) corrected by Georg Fischer, Aug 28 2020