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Search: id:A003107
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| A003107 |
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Number of partitions of n into Fibonacci parts (with a single type of 1).
(Formerly M0556)
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+0
9
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| 1, 1, 2, 3, 4, 6, 8, 10, 14, 17, 22, 27, 33, 41, 49, 59, 71, 83, 99, 115, 134, 157, 180, 208, 239, 272, 312, 353, 400, 453, 509, 573, 642, 717, 803, 892, 993, 1102, 1219, 1350, 1489, 1640, 1808, 1983, 2178, 2386, 2609, 2854, 3113, 3393, 3697, 4017, 4367, 4737
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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
A098641(n) = a(A000045(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 24 2005
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
G. Almkvist, Partitions with Parts in a Finite Set and with Parts Outside a Finite Set, Exper. Math. vol 11 no 4 (2002) p 449-456
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FORMULA
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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
G.f.: Product(1/(1-x^fibonacci(i)), i=2..infinity). - Ron Knott (ron(AT)ronknott.com), Oct 22 2003
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]
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EXAMPLE
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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
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MATHEMATICA
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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)
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CROSSREFS
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Cf. A007000, A005092, A003107, A028290 (where the only Fibonacci numbers allowed are 1, 2, 3, 5 and 8).
Cf. A102848.
A000119. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 11 2009]
Sequence in context: A027589 A039851 A028290 this_sequence A014977 A008583 A053253
Adjacent sequences: A003104 A003105 A003106 this_sequence A003108 A003109 A003110
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Herman P. Robinson
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 21 2002
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