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Search: id:A102848
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| A102848 |
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Number of partitions of n into Fibonacci number of integer parts. |
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+0
3
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| 1, 2, 3, 4, 6, 8, 10, 14, 18, 23, 29, 37, 47, 59, 74, 92, 114, 141, 173, 213, 261, 318, 387, 470, 569, 687, 827, 994, 1192, 1426, 1702, 2028, 2412, 2863, 3392, 4012, 4738, 5585, 6574, 7726, 9067, 10624, 12433, 14528, 16957, 19763, 23007, 26749, 31067, 36034
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OFFSET
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1,2
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COMMENT
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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)
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FORMULA
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G.f.: Sum(x^Fibonacci(n)/Product(1-x^i, i = 1 .. Fibonacci(n)), n = 2 = .. infinity). - Jovovic
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EXAMPLE
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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.
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CROSSREFS
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Cf. A000040, A000045, A003107.
Sequence in context: A008583 A053253 A095913 this_sequence A134157 A045476 A066816
Adjacent sequences: A102845 A102846 A102847 this_sequence A102849 A102850 A102851
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KEYWORD
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easy,nonn
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AUTHOR
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Lior Manor (lior.manor(AT)gmail.com) Feb 28 2005
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EXTENSIONS
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More terms and g.f. from Vladeta Jovovic, Mar 02 2005
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