%I A000121 M0249 N0088
%S A000121 1,2,2,3,3,3,4,3,4,5,4,5,4,4,6,5,6,6,5,6,4,5,7,6,8,7,6,8,6,7,8,6,7,5,5,
%T A000121 8,7,9,9,8,10,7,8,10,8,10,8,7,10,8,9,9,7,8,5,6,9,8,11,10,9,12,9,11,13,
%U A000121 10,12,9,8,12,10,12,12,10,12,8,9,12,10,13,11,9,12,9,10,11,8,9,6,6,10,9
%N A000121 Number of representations of n as a sum of Fibonacci numbers (1 is allowed 
               twice as a part).
%C A000121 Number of partitions into distinct Fibonacci parts (1 counted as two 
               distinct Fibonacci numbers).
%C A000121 Inverse Euler transform of sequence has generating function sum_{n>0} 
               x^F(n)-x^{2F(n)} where F() is Fibonacci.
%D A000121 D. A. Klarner, Representations of N as a sum of distinct elements from 
               special sequences, Fib. Quart., 4 (1966), 289-306 and 322.
%D A000121 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000121 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000121 T. D. Noe, <a href="b000121.txt">Table of n, a(n) for n = 0..6765</a>
%p A000121 with(combinat): p := product((1+x^fibonacci(i)), i=1..25): s := series(p,
               x,1000): for k from 0 to 250 do printf(`%d,`,coeff(s,x,k)) od:
%o A000121 (PARI) a(n)=local(A,m,f); if(n<0,0,A=1+x*O(x^n); m=1; while((f=fibonacci(m))<=n,
               A*=1+x^f; m++); polcoeff(A,n))
%Y A000121 Cf. A000119. Least inverse is A083853.
%Y A000121 Sequence in context: A072789 A126302 A134674 this_sequence A049846 A086712 
               A125842
%Y A000121 Adjacent sequences: A000118 A000119 A000120 this_sequence A000122 A000123 
               A000124
%K A000121 nonn
%O A000121 0,2
%A A000121 N. J. A. Sloane (njas(AT)research.att.com).
%E A000121 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 18 2000