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A161027
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Number of partitions of n into Fibonacci numbers where every part appears at least 3 times
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1
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0, 0, 1, 1, 1, 2, 1, 2, 3, 3, 3, 6, 5, 6, 10, 8, 9, 14, 13, 16, 20, 19, 23, 30, 30, 33, 41, 43, 48, 59, 58, 67, 78, 81, 92, 105, 109, 123, 140, 148, 160, 182, 193, 214, 238, 249, 275, 305, 322, 353, 386, 413, 447, 490, 520, 561, 611, 650, 701, 762, 804, 868, 938, 997, 1067, 1147
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OFFSET
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1,6
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LINKS
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R. H. Hardin, Table of n, a(n) for n=1..1000
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FORMULA
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Contribution from Emeric Deutsch, Jun 23 2009: (Start)
G.f.=-1+Product(1+x^{3*F(j)}/(1-x^{F(j)}), j=2..infinity), where F(j) =A000045(j) are the Fibonacci numbers (F(0)=0, F(1)=1).
(End)
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EXAMPLE
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Contribution from Emeric Deutsch, Jun 23 2009: (Start)
a(10)=3 because we have 22222, 2221111, and 1^(10).
(End)
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MAPLE
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with(combinat): g := -1+product(1+x^(3*fibonacci(j))/(1-x^fibonacci(j)), j = 2 .. 10): gser := series(g, x = 0, 95): seq(coeff(gser, x, n), n = 2 .. 71); [From Emeric Deutsch, Jun 23 2009]
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CROSSREFS
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Sequence in context: A183202 A161308 A161242 * A161078 A161294 A161269
Adjacent sequences: A161024 A161025 A161026 * A161028 A161029 A161030
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin Jun 02 2009
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STATUS
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approved
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