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)).

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, 48, 51, 52, 55, 56, 59, 60, 63, 64, 67, 68, 71, 72, 75, 76, 79, 80, 83, 84, 87, 88, 91, 92, 95, 96, 99, 100, 103, 104, 107, 108, 111, 112, 115, 116, 119, 120, 123, 124, 127, 128

Offset: 0

Author

N. J. A. Sloane, Feb 17 2002

Keywords

• nonn
• easy

References

• R. K. Guy, Unsolved Problems in Number Theory, E27.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A067017, A067018.

Programs

Haskell

a067016 n = a067016_list !! n
a067016_list = [1,4,3,2] ++ f [2,3,4,1] where
   f xs = maxi : f (maxi : xs) where
     maxi = maximum $ zipWith (+) xs (reverse xs)
-- Reinhard Zumkeller, May 05 2012

Formula

First differences are ultimately periodic.

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

Extensions

More terms from John W. Layman, Feb 20 2002