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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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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; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| Fielder, Daniel C.; Special integer sequences controlled by three parameters. Fibonacci Quart 6 1968 64-70.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| 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
| 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
| 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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PROG
| (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
| Cf. A000570.
Sequence in context: A010460 A152399 A022822 * A162207 A092614 A085899
Adjacent sequences: A001636 A001637 A001638 * A001640 A001641 A001642
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by Michael Somos, Feb 17, 2002
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