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A067016 Start with a(0)=1, a(1)=4, a(2)=3, a(3)=2; for n>=3, a(n+1) = max_i (a(i)+a(n-i)).

%I A067016 #18 Dec 14 2023 05:23:58
%S A067016 1,4,3,2,7,8,11,12,15,16,19,20,23,24,27,28,31,32,35,36,39,40,43,44,47,
%T A067016 48,51,52,55,56,59,60,63,64,67,68,71,72,75,76,79,80,83,84,87,88,91,92,
%U A067016 95,96,99,100,103,104,107,108,111,112,115,116,119,120,123,124,127,128
%N A067016 Start with a(0)=1, a(1)=4, a(2)=3, a(3)=2; for n>=3, a(n+1) = max_i (a(i)+a(n-i)).
%D A067016 R. K. Guy, Unsolved Problems in Number Theory, E27.
%H A067016 Reinhard Zumkeller, <a href="/A067016/b067016.txt">Table of n, a(n) for n = 0..1000</a>
%F A067016 First differences are ultimately periodic.
%F A067016 Conjecture: a(n) = (-3+(-1)^n+4*n)/2 for n>3. G.f.: -(2*x^6 -2*x^5 -6*x^4 +4*x^3 +2*x^2 -3*x -1) / ((x -1)^2*(x +1)). - _Colin Barker_, Apr 01 2013
%o A067016 (Haskell)
%o A067016 a067016 n = a067016_list !! n
%o A067016 a067016_list = [1,4,3,2] ++ f [2,3,4,1] where
%o A067016    f xs = maxi : f (maxi : xs) where
%o A067016      maxi = maximum $ zipWith (+) xs (reverse xs)
%o A067016 -- _Reinhard Zumkeller_, May 05 2012
%Y A067016 Cf. A067017, A067018.
%K A067016 nonn,easy
%O A067016 0,2
%A A067016 _N. J. A. Sloane_, Feb 17 2002
%E A067016 More terms from _John W. Layman_, Feb 20 2002