A064651 a(n) = ceiling(a(n-1)/2) + a(n-2) with a(0)=0 and a(1)=1.

0, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 15, 20, 25, 33, 42, 54, 69, 89, 114, 146, 187, 240, 307, 394, 504, 646, 827, 1060, 1357, 1739, 2227, 2853, 3654, 4680, 5994, 7677, 9833, 12594, 16130, 20659, 26460, 33889, 43405, 55592, 71201, 91193, 116798, 149592

Offset: 0

Author

Henry Bottomley, Oct 04 2001

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..9300

Crossrefs

Cf. A064324, A064325.

Cf. A064650, A000045, A188934.

Programs

Haskell

a064651 n = a064651_list !! n
a064651_list = 0 : 1 : zipWith (+)
   a064651_list (map (flip div 2 . (+ 1)) $ tail a064651_list)
-- Reinhard Zumkeller, Apr 30 2015

Mathematica

RecurrenceTable[{a[0]==0, a[1]==1, a[n]==Ceiling[a[n-1]/2]+a[n-2]}, a, {n,50}] (* Harvey P. Dale, Aug 22 2012 *)
t = {0, 1}; Do[AppendTo[t, Ceiling[t[[-1]]/2] + t[[-2]]], {48}]; t (* T. D. Noe, Aug 22 2012 *)

Formula

a(n) = A064650(n) - 1.

Lim_{n->infinity} a(n)/a(n-1) = (1+sqrt(17))/4 = 1.2807764... = A188934.