A022908 - OEIS

%I #30 Jun 09 2022 02:28:38

%S 0,2,5,11,20,35,56,86,125,179,248,338,449,590,761,971,1220,1523,1880,

%T 2306,2801,3386,4061,4847,5744,6782,7961,9311,10832,12563,14504,16694,

%U 19133,21875,24920,28322,32081,36266,40877,45983,51584

%N The sequence M(n) in A022905.

%H T. D. Noe, <a href="/A022908/b022908.txt">Table of n, a(n) for n = 1..1000</a>

%H J. M. Dover, <a href="http://arxiv.org/abs/1606.08033">On two OEIS conjectures</a>, arXiv:1606.08033 [math.CO], 2016.

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

%F a(1) = 0; a(n) = (1+3*A033485(2*n-3))/2 = A022905(n-1)+1, n > 1. - _Philippe Deléham_, May 30 2006

%t (* 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]];

%t a[1] = 0; a[n_] := b[n-1] + 1;

%t Array[a, 50] (* _Jean-François Alcover_, Nov 11 2018 *)

%o (Python)

%o from itertools import islice

%o from collections import deque

%o def A022908_gen(): # generator of terms

%o     aqueue, f, b, a = deque([2]), True, 1, 2

%o     yield from (0,2)

%o     while True:

%o         a += b

%o         aqueue.append(a)

%o         if f:

%o             yield (3*a+1)//2

%o             b = aqueue.popleft()

%o         f = not f

%o A022908_list = list(islice(A022908_gen(),40)) # _Chai Wah Wu_, Jun 08 2022

%K nonn

%O 1,2

%A _Clark Kimberling_