|
|
A064651
|
|
a(n) = ceiling(a(n-1)/2) + a(n-2) with a(0)=0 and a(1)=1.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
Lim_{n->infinity} a(n)/a(n-1) = (1+sqrt(17))/4 = 1.2807764... = A188934.
|
|
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 *)
|
|
PROG
|
(Haskell)
a064651 n = a064651_list !! n
a064651_list = 0 : 1 : zipWith (+)
a064651_list (map (flip div 2 . (+ 1)) $ tail a064651_list)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|