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Search: id:A001639
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| A001639 |
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A Fielder sequence. a(n)=a(n-1)+a(n-3)+a(n-4)+a(n-5), n>=6.
(Formerly M3353 N1349)
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+0
1
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| 1, 1, 4, 9, 16, 22, 36, 65, 112, 186, 309, 522, 885, 1492, 2509, 4225, 7124, 12010, 20236, 34094, 57453, 96823, 163163, 274946, 463316, 780755, 1315687, 2217112, 3736129, 6295887, 10609441, 17878369, 30127497, 50768954, 85552651, 144167958, 242942778
(list; graph; listen)
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OFFSET
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1,3
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Fielder, Daniel C.; Special integer sequences controlled by three parameters. Fibonacci Quart 6 1968 64-70.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: x*(1+3*x^2+4*x^3+5*x^4)/(1-x-x^3-x^4-x^5).
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MAPLE
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A001639:=-(1+3*z**2+4*z**3+5*z**4)/(-1+z+z**3+z**4+z**5); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
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Drop[CoefficientList[Series[x*(1+3*x^2+4*x^3+5*x^4)/(1-x-x^3-x^4-x^5), {x, 0, 40}], x], 1] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 10 2006
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(x*(1+3*x^2+4*x^3+5*x^4)/(1-x-x^3-x^4-x^5)+x*O(x^n), n))
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CROSSREFS
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Cf. A000570.
Sequence in context: A010460 A152399 A022822 this_sequence A092614 A085899 A027874
Adjacent sequences: A001636 A001637 A001638 this_sequence A001640 A001641 A001642
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Michael Somos, Feb 17, 2002
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