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A007000
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Number of partitions of n into Fibonacci parts (with 2 types of 1).
(Formerly M1045)
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3
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1, 2, 4, 7, 11, 17, 25, 35, 49, 66, 88, 115, 148, 189, 238, 297, 368, 451, 550, 665, 799, 956, 1136, 1344, 1583, 1855, 2167, 2520, 2920, 3373, 3882, 4455, 5097, 5814, 6617, 7509, 8502, 9604, 10823, 12173, 13662, 15302, 17110, 19093, 21271, 23657, 26266
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
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FORMULA
| a(n)=1/n*Sum_{k=1..n} (A005092(k)+1)*a(n-k), n > 1, a(0)=1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 22 2002
G.f.=1/product(1-x^fibonacci(j), j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 05 2006
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EXAMPLE
| a(2)=4 because we have [2],[1',1'],[1',1],[1,1] (the two types of 1 are denoted 1 and 1').
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MAPLE
| with(combinat): gf := 1/product((1-q^fibonacci(k)), k=1..20): s := series(gf, q, 200): for i from 0 to 199 do printf(`%d, `, coeff(s, q, i)) od:
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MATHEMATICA
| CoefficientList[ Series[ 1/Product[1 - x^Fibonacci[i], {i, 1, 15}], {x, 0, 50}], x]
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CROSSREFS
| Cf. A003107.
Sequence in context: A067997 A175491 A034379 * A073472 A096914 A004250
Adjacent sequences: A006997 A006998 A006999 * A007001 A007002 A007003
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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EXTENSIONS
| More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Feb 08, 2002
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