A022907 The sequence m(n) in A022905.

0, 2, 5, 8, 14, 20, 29, 38, 53, 68, 89, 110, 140, 170, 209, 248, 302, 356, 425, 494, 584, 674, 785, 896, 1037, 1178, 1349, 1520, 1730, 1940, 2189, 2438, 2741, 3044, 3401, 3758, 4184, 4610, 5105, 5600, 6185, 6770, 7445, 8120, 8906, 9692, 10589

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

a123[n_] := a123[n] = If[n == 0, 1, a123[Floor[n/2]] + a123[n-1]];
a[n_] := If[n == 1, 0, (3/2) a123[n-1] - 1]; Array[a, 50] (* Jean-François Alcover, Dec 04 2018 *)

Python

from itertools import islice
from collections import deque
def A022907_gen(): # generator of terms
    aqueue, f, b, a = deque([2]), True, 1, 2
    yield from (0, 2, 5)
    while True:
        a += b
        yield 3*a-1
        aqueue.append(a)
        if f: b = aqueue.popleft()
        f = not f
A022907_list = list(islice(A022907_gen(),40)) # Chai Wah Wu, Jun 08 2022

Formula

a(n) = 3 * A033485(n-1) - 1 = (3/2) * A000123(n-1) - 1, n>1. Proved by Jeremy Dover. - Ralf Stephan, Dec 08 2004