A022908 The sequence M(n) in A022905.

0, 2, 5, 11, 20, 35, 56, 86, 125, 179, 248, 338, 449, 590, 761, 971, 1220, 1523, 1880, 2306, 2801, 3386, 4061, 4847, 5744, 6782, 7961, 9311, 10832, 12563, 14504, 16694, 19133, 21875, 24920, 28322, 32081, 36266, 40877, 45983, 51584

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• J. M. Dover, On two OEIS conjectures, arXiv:1606.08033 [math.CO], 2016.

Programs

Mathematica

(* b = A022905 *) b[1] = 1; b[n_] := b[n] = b[n-1] + 1 + If[EvenQ[n], 2 b[n/2], b[(n-1)/2] + b[(n+1)/2]];
a[1] = 0; a[n_] := b[n-1] + 1;
Array[a, 50] (* Jean-François Alcover, Nov 11 2018 *)

Python

from itertools import islice
from collections import deque
def A022908_gen(): # generator of terms
    aqueue, f, b, a = deque([2]), True, 1, 2
    yield from (0,2)
    while True:
        a += b
        aqueue.append(a)
        if f:
            yield (3*a+1)//2
            b = aqueue.popleft()
        f = not f
A022908_list = list(islice(A022908_gen(),40)) # Chai Wah Wu, Jun 08 2022

Formula

a(n) = n + Sum_{k=1..n-1} A022907(k), n > 1. [corrected by Sean A. Irvine, May 22 2019]

a(1) = 0; a(n) = (1+3*A033485(2*n-3))/2 = A022905(n-1)+1, n > 1. - Philippe Deléham, May 30 2006