%I A003107 M0556
%S A003107 1,1,2,3,4,6,8,10,14,17,22,27,33,41,49,59,71,83,99,115,134,157,180,208,
%T A003107 239,272,312,353,400,453,509,573,642,717,803,892,993,1102,1219,1350,
%U A003107 1489,1640,1808,1983,2178,2386,2609,2854,3113,3393,3697,4017,4367,4737
%N A003107 Number of partitions of n into Fibonacci parts (with a single type of 
               1).
%C A003107 The partitions allow repeated items but the order of items is immaterial 
               (1+2=2+1) - Ron Knott (ron(AT)ronknott.com), Oct 22 2003
%C A003107 A098641(n) = a(A000045(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 24 2005
%D A003107 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003107 T. D. Noe, <a href="b003107.txt">Table of n, a(n) for n=0..1000</a>
%H A003107 G. Almkvist, <a href="http://projecteuclid.org/euclid.em/1057864654">
               Partitions with Parts in a Finite Set and with Parts Outside a Finite 
               Set</a>, Exper. Math. vol 11 no 4 (2002) p 449-456
%F A003107 a(n)=(1/n)*Sum_{k=1..n} A005092(k)*a(n-k), n > 1, a(0)=1. - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Jan 21 2002
%F A003107 G.f.: Product(1/(1-x^fibonacci(i)), i=2..infinity). - Ron Knott (ron(AT)ronknott.com), 
               Oct 22 2003
%F A003107 a(n) = f(n,1,1) with f(x,y,z) = if x<y then 0^x else f(x-y,y,z)+f(x,y+z,
               y). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 
               11 2009]
%e A003107 a(4)=4 since the 4 partitions of 4 using only Fibonacci numbers, reptitions 
               allowed, are 1+1+1+1, 2+2, 2+1+1, 3+1
%t A003107 CoefficientList[ Series[1/ Product[1 - x^Fibonacci[i], {i, 2, 21}], {x, 
               0, 53}], x] (from Robert G. Wilson v (rgwv(at)rgwv.com), Mar 28 2006)
%Y A003107 Cf. A007000, A005092, A003107, A028290 (where the only Fibonacci numbers 
               allowed are 1, 2, 3, 5 and 8).
%Y A003107 Cf. A102848.
%Y A003107 A000119. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Nov 11 2009]
%Y A003107 Sequence in context: A027589 A039851 A028290 this_sequence A014977 A008583 
               A053253
%Y A003107 Adjacent sequences: A003104 A003105 A003106 this_sequence A003108 A003109 
               A003110
%K A003107 nonn,easy,new
%O A003107 0,3
%A A003107 N. J. A. Sloane (njas(AT)research.att.com), Herman P. Robinson
%E A003107 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 21 2002