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A098641
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Number of partitions of the n-th Fibonacci number into Fibonacci numbers.
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6
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1, 1, 2, 3, 6, 14, 41, 157, 803, 5564, 53384, 718844, 13783708, 380676448, 15298907733, 902438020514, 78720750045598, 10220860796171917, 1986422867300209784, 580763241873718042562, 256553744608217295298827
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) = A003107(A000045(n)).
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FORMULA
| a(n) = A098642(n) + A098643(n) + A098644(n).
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EXAMPLE
| n=6: A000045(6)=8, a(6) = #{8, 5+3, 5+2+1, 5+1+1+1, 3+3+2, 3+3+1+1, 3+2+2+1, 3+2+1+1+1, 3+1+1+1+1+1, 2+2+2+2, 2+2+2+1+1, 2+2+1+1+1+1, 2+1+1+1+1+1+1, 1+1+1+1+1+1+1+1} = 14, the other partitions of 8 into parts with at least one non-Fibonacci number: 7+1, 6+2, 6+1+1, 4+4, 4+3+1, 4+2+2, 4+2+1+1 and 4+1+1+1+1.
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MATHEMATICA
| cl = CoefficientList[ Series[1/Product[(1 - x^Fibonacci[i]), {i, 2, 21}], {x, 0, 10950}], x]; cl[[ Table[ Fibonacci[i] + 1, {i, 21}] ]] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 25 2005)
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CROSSREFS
| Cf. A000041, A000045, A065033, A072214, A098642-A098644.
Sequence in context: A081293 A193215 A007611 * A188775 A056569 A094468
Adjacent sequences: A098638 A098639 A098640 * A098642 A098643 A098644
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KEYWORD
| nonn
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AUTHOR
| Marcel Dubois de Cadouin (dubois.ml(AT)club-internet.fr), Oct 27 2004
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EXTENSIONS
| Corrected and extended by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 24 2005
a(15)-a(21) from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 25 2005
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Mar 29 2006
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