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

1,2

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) = 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

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 *)

Prog

(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

Crossrefs

Sequence in context: A139482 A038377 A261227 * A256310 A026390 A005575

Adjacent sequences: A022905 A022906 A022907 * A022909 A022910 A022911

Keyword

nonn

Author

Clark Kimberling

Status

approved