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A001642
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A Fielder sequence.
(Formerly M2367 N0937)
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5
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1, 3, 4, 11, 21, 36, 64, 115, 211, 383, 694, 1256, 2276, 4126, 7479, 13555, 24566, 44523, 80694, 146251, 265066, 480406, 870689, 1578040, 2860046, 5183558, 9394699, 17026986, 30859771, 55930361, 101368389, 183720435, 332975581, 603486148, 1093760479
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OFFSET
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1,2
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REFERENCES
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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
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FORMULA
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G.f.: x(1+2x+4x^3+5x^4)/(1-x-x^2-x^4-x^5).
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MAPLE
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A001642:=-(z+1)*(5*z**3-z**2+z+1)/(-1+z+z**2+z**4+z**5); # conjectured by Simon Plouffe in his 1992 dissertation
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MATHEMATICA
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LinearRecurrence[{1, 1, 0, 1, 1}, {1, 3, 4, 11, 21}, 50] (* T. D. Noe, Aug 09 2012 *)
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PROG
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(PARI) a(n)=if(n<0, 0, polcoeff(x*(1+2*x+4*x^3+5*x^4)/(1-x-x^2-x^4-x^5)+x*O(x^n), n))
(Magma) I:=[1, 3, 4, 11, 21]; [n le 5 select I[n] else Self(n-1) + Self(n-2) + Self(n-4) + Self(n-5): n in [1..30]]; // G. C. Greubel, Jan 09 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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