%I A035517
%S A035517 0,1,2,3,1,3,5,1,5,2,5,8,1,8,2,8,3,8,1,3,8,13,1,13,2,13,3,13,1,3,13,5,
%T A035517 13,1,5,13,2,5,13,21,1,21,2,21,3,21,1,3,21,5,21,1,5,21,2,5,21,8,21,1,8,
%U A035517 21,2,8,21,3,8,21,1,3,8,21,34,1,34,2,34,3,34,1,3,34,5,34,1,5,34,2,5,34
%N A035517 Triangular array read by rows, formed from Zeckendorf expansion of integers: 
               repeatedly subtract the largest Fibonacci number you can until nothing 
               remains. Row n give Z. expansion of n.
%C A035517 Row n has A007895(n) terms.
%D A035517 D. E. Knuth, Fibonacci multiplication, Appl. Math. Lett. 1 (1988), 57-60.
%D A035517 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.
%H A035517 T. D. Noe, <a href="b035517.txt">Rows n=0..1000 of triangle, flattened</
               a>
%H A035517 N. J. A. Sloane, <a href="classic.html#WYTH">Classic Sequences</a>
%e A035517 0=0; 1=1; 2=2; 3=3; 4=1+3; 5=5; 6=1+5; 7=2+5; 8=8; 9=1+8; 10=2+8; ... 
               so triangle begins
%e A035517 0
%e A035517 1
%e A035517 2
%e A035517 3
%e A035517 1 3
%e A035517 5
%e A035517 1 5
%e A035517 2 5
%e A035517 8
%e A035517 1 8
%e A035517 2 8
%e A035517 3 8
%e A035517 1 3 8
%Y A035517 Cf. A014417, A007895, A035514, A035515, A035516.
%Y A035517 Sequence in context: A119348 A050375 A154722 this_sequence A099471 A121775 
               A127951
%Y A035517 Adjacent sequences: A035514 A035515 A035516 this_sequence A035518 A035519 
               A035520
%K A035517 nonn,easy,tabf,nice
%O A035517 0,3
%A A035517 N. J. A. Sloane (njas(AT)research.att.com).
%E A035517 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 13 1999