Search: id:A102848
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%I A102848
%S A102848 1,2,3,4,6,8,10,14,18,23,29,37,47,59,74,92,114,141,173,213,261,318,387,
               470,
%T A102848 569,687,827,994,1192,1426,1702,2028,2412,2863,3392,4012,4738,5585,6574,
%U A102848 7726,9067,10624,12433,14528,16957,19763,23007,26749,31067,36034
%N A102848 Number of partitions of n into Fibonacci number of integer parts.
%C A102848 A003107 & this sequence are different sequences. A003107 gives the number 
               of partitions in which each part of n is a Fibonacci number, this 
               sequence gives the number of partitions in which the number of parts 
               is a Fibonacci number. Both sequences share the same values for the 
               first 8 values. For example A003107(4) = 4 because of the following 
               4 partitions of 5: (3,1), (2,2), (2,1,1), (1,1,1,1) whereas a(4) 
               is also 4 but because of different set of partitions: (4), (3,1), 
               (2,2), (2,1,1)
%F A102848 G.f.: Sum(x^Fibonacci(n)/Product(1-x^i, i = 1 .. Fibonacci(n)), n = 2 
               = .. infinity). - Jovovic
%e A102848 a(5) = 6 since out of 7 possible partitions of 5 into integer parts, 
               only 6 include a Fibonacci number of parts: (5), (4,1), (3,2), (3,
               1,1), (2,2,1), (1,1,1,1,1). The 7th integer partitions pf 5 (2,1,
               1,1) is not counted since it includes 4 integer parts and 4 is not 
               a Fibonacci number.
%Y A102848 Cf. A000040, A000045, A003107.
%Y A102848 Sequence in context: A008583 A053253 A095913 this_sequence A134157 A045476 
               A066816
%Y A102848 Adjacent sequences: A102845 A102846 A102847 this_sequence A102849 A102850 
               A102851
%K A102848 easy,nonn
%O A102848 1,2
%A A102848 Lior Manor (lior.manor(AT)gmail.com) Feb 28 2005
%E A102848 More terms and g.f. from Vladeta Jovovic, Mar 02 2005

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