|
| |
|
|
A035516
|
|
Triangular array formed from Zeckendorf expansion of integers: repeatedly subtract the largest Fibonacci number you can until nothing remains.
|
|
13
|
|
|
|
0, 1, 2, 3, 3, 1, 5, 5, 1, 5, 2, 8, 8, 1, 8, 2, 8, 3, 8, 3, 1, 13, 13, 1, 13, 2, 13, 3, 13, 3, 1, 13, 5, 13, 5, 1, 13, 5, 2, 21, 21, 1, 21, 2, 21, 3, 21, 3, 1, 21, 5, 21, 5, 1, 21, 5, 2, 21, 8, 21, 8, 1, 21, 8, 2, 21, 8, 3, 21, 8, 3, 1, 34, 34, 1, 34, 2, 34, 3, 34, 3, 1, 34, 5, 34, 5, 1, 34, 5, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Row n has A007895(n) terms.
|
|
|
REFERENCES
|
Zeckendorf, E., Representation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liege 41, 179-182, 1972.
|
|
|
LINKS
|
T. D. Noe, Rows n=0..1000 of triangle, flattened
N. J. A. Sloane, Classic Sequences
|
|
|
EXAMPLE
|
16 = 13 + 3.
0; 1; 2; 3; 3,1; 5; 5,1; 5,2; 8; 8,1; 8,2; ...
|
|
|
PROG
|
(Haskell)
a035516 n k = a035516_tabf !! n !! k
a035516_tabf = map a035516_row [0..]
a035516_row 0 = [0]
a035516_row n = z n $ reverse $ takeWhile (<= n) a000045_list where
z 0 _ = []
z x (f:fs'@(_:fs)) = if f <= x then f : z (x - f) fs else z x fs'
-- Reinhard Zumkeller, Mar 10 2013
|
|
|
CROSSREFS
|
Cf. A035517, A035514, A035515.
Cf. A000045.
Sequence in context: A077990 A085667 A220114 * A120428 A079950 A174953
Adjacent sequences: A035513 A035514 A035515 * A035517 A035518 A035519
|
|
|
KEYWORD
|
nonn,easy,tabf
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
EXTENSIONS
|
More terms from James A. Sellers, Dec 13 1999
|
|
|
STATUS
|
approved
|
| |
|
|
