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%I #24 Jun 08 2022 16:22:45
%S 1,4,10,19,34,55,85,124,178,247,337,448,589,760,970,1219,1522,1879,
%T 2305,2800,3385,4060,4846,5743,6781,7960,9310,10831,12562,14503,16693,
%U 19132,21874,24919,28321,32080,36265,40876,45982,51583,57769
%N a(n) = M(n) + m(n) for n >= 2, where M(n) = max{ a(i) + a(n-i): i = 1..n-1 }, m(n) = min{ a(i) + a(n-i): i = 1..n-1 }.
%H T. D. Noe, <a href="/A022905/b022905.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 n + sum(k=2, n, A022907(n)).
%F a(n+1) = 1+3*Sum_{k=1..n} A033485(k). - _Philippe Deléham_, Jun 17 2010
%F a(n) = a(n-1) + 1 + a(floor(n/2)) + a(ceiling(n/2))) for n>1, a(1) = 1. - _Alois P. Heinz_, Sep 17 2013
%F a(n+1) = (3*A033485(2n+1)-1)/2. - _Chai Wah Wu_, Jun 08 2022
%p a:= proc(n) option remember; `if`(n=1, 1,
%p a(n-1)+1+a(floor(n/2))+a(ceil(n/2)))
%p end:
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Sep 17 2013
%t a[n_] := a[n] = If[n==1, 1, a[n-1]+1+a[Floor[n/2]]+a[Ceiling[n/2]]]; Array[a,100] (* _Jean-François Alcover_, Aug 07 2017, after _Alois P. Heinz_ *)
%o (Python)
%o from itertools import islice
%o from collections import deque
%o def A022905_gen(): # generator of terms
%o aqueue, f, b, a = deque([2]), True, 1, 2
%o yield 1
%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 A022905_list = list(islice(A022905_gen(),40)) # _Chai Wah Wu_, Jun 08 2022
%Y Cf. A022907, A022908.
%K nonn
%O 1,2
%A _Clark Kimberling_
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