%I A112309
%S A112309 1,2,1,2,1,3,2,3,1,2,3,2,5,1,2,5,1,3,5,2,3,5,1,2,3,5,1,3,8,2,3,8,1,2,3,
%T A112309 8,2,5,8,1,2,5,8,1,3,5,8,2,3,5,8,1,2,3,5,8,2,5,13,1,2,5,13,1,3,5,13,2,
               3,
%U A112309 5,13,1,2,3,5,13,1,3,8,13,2,3,8,13,1,2,3,8,13,2,5,8,13,1,2,5,8,13,1,3
%N A112309 Triangle read by rows: row n gives terms in lazy Fibonacci representation 
               of n.
%C A112309 Write n as a sum c_2 F_2 + c_3 F_3 + ..., where the F_i are Fibonacci 
               numbers and the c_i are 0 or 1. The lazy expansion is the minimal 
               one in the lexicographic order, in contrast to the Zeckendorf expansion 
               (A035517, A007895), which is the maximal one.
%C A112309 In other words we give preference to the smallest Fibonacci numbers.
%D A112309 W. Steiner, The joint distribution of greedy and lazy Fibonacci expansions, 
               Fib. Q., 43 (No. 1, 2005), 60-69.
%e A112309 Triangle begins:
%e A112309 1 meaning 1 = 1
%e A112309 2 meaning 2 = 2
%e A112309 1 2 meaning 3 = 1+2
%e A112309 1 3 meaning 4 = 1+3
%e A112309 2 3 meaning 5 = 2+3
%e A112309 1 2 3 meaning 6 = 1+2+3 (and not the Zeckendorf expansion 1+5)
%e A112309 2 5 meaning 7 = 2+5
%Y A112309 Cf. A000045, A112310, A035517, A007895.
%Y A112309 Sequence in context: A157235 A086289 A077807 this_sequence A160006 A060682 
               A093873
%Y A112309 Adjacent sequences: A112306 A112307 A112308 this_sequence A112310 A112311 
               A112312
%K A112309 nonn,tabf,easy
%O A112309 1,2
%A A112309 N. J. A. Sloane (njas(AT)research.att.com), Dec 01 2005
%E A112309 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 01 2005