cp's OEIS Frontend

A022905 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 }.

%I A022905 #27 Dec 31 2024 20:16:28
%S A022905 1,4,10,19,34,55,85,124,178,247,337,448,589,760,970,1219,1522,1879,
%T A022905 2305,2800,3385,4060,4846,5743,6781,7960,9310,10831,12562,14503,16693,
%U A022905 19132,21874,24919,28321,32080,36265,40876,45982,51583,57769
%N A022905 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 A022905 T. D. Noe, <a href="/A022905/b022905.txt">Table of n, a(n) for n=1..1000</a>
%H A022905 J. M. Dover, <a href="http://arxiv.org/abs/1606.08033">On two OEIS conjectures</a>, arXiv:1606.08033 [math.CO], 2016.
%F A022905 a(n) = n + Sum_{k=2..n} A022907(k).
%F A022905 a(n+1) = 1+3*Sum_{k=1..n} A033485(k). - _Philippe Deléham_, Jun 17 2010
%F A022905 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 A022905 a(n+1) = (3*A033485(2n+1)-1)/2. - _Chai Wah Wu_, Jun 08 2022
%p A022905 a:= proc(n) option remember; `if`(n=1, 1,
%p A022905       a(n-1)+1+a(floor(n/2))+a(ceil(n/2)))
%p A022905     end:
%p A022905 seq(a(n), n=1..100);  # _Alois P. Heinz_, Sep 17 2013
%t A022905 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 A022905 (Python)
%o A022905 from itertools import islice
%o A022905 from collections import deque
%o A022905 def A022905_gen(): # generator of terms
%o A022905     aqueue, f, b, a = deque([2]), True, 1, 2
%o A022905     yield 1
%o A022905     while True:
%o A022905         a += b
%o A022905         aqueue.append(a)
%o A022905         if f:
%o A022905             yield (3*a-1)//2
%o A022905             b = aqueue.popleft()
%o A022905         f = not f
%o A022905 A022905_list = list(islice(A022905_gen(),40)) # _Chai Wah Wu_, Jun 08 2022
%Y A022905 Cf. A022907, A022908.
%K A022905 nonn
%O A022905 1,2
%A A022905 _Clark Kimberling_