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

1,2

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.

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A111711 A095348 A215725 * A006918 A274523 A165189

Adjacent sequences: A022904 A022905 A022906 * A022908 A022909 A022910

Keyword

nonn

Author

Clark Kimberling

Status

approved