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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 }.
3
1, 4, 10, 19, 34, 55, 85, 124, 178, 247, 337, 448, 589, 760, 970, 1219, 1522, 1879, 2305, 2800, 3385, 4060, 4846, 5743, 6781, 7960, 9310, 10831, 12562, 14503, 16693, 19132, 21874, 24919, 28321, 32080, 36265, 40876, 45982, 51583, 57769
OFFSET
1,2
LINKS
J. M. Dover, On two OEIS conjectures, arXiv:1606.08033 [math.CO], 2016.
FORMULA
n + sum(k=2, n, A022907(n)).
a(n+1) = 1+3*Sum_{k=1..n} A033485(k). - Philippe Deléham, Jun 17 2010
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
a(n+1) = (3*A033485(2n+1)-1)/2. - Chai Wah Wu, Jun 08 2022
MAPLE
a:= proc(n) option remember; `if`(n=1, 1,
a(n-1)+1+a(floor(n/2))+a(ceil(n/2)))
end:
seq(a(n), n=1..100); # Alois P. Heinz, Sep 17 2013
MATHEMATICA
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 *)
PROG
(Python)
from itertools import islice
from collections import deque
def A022905_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield 1
while True:
a += b
aqueue.append(a)
if f:
yield (3*a-1)//2
b = aqueue.popleft()
f = not f
A022905_list = list(islice(A022905_gen(), 40)) # Chai Wah Wu, Jun 08 2022
CROSSREFS
Sequence in context: A301182 A301194 A015616 * A155368 A301155 A301215
KEYWORD
nonn
STATUS
approved