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A001643
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A Fielder sequence.
(Formerly M2368 N0938)
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2
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1, 3, 4, 11, 21, 42, 71, 131, 238, 443, 815, 1502, 2757, 5071, 9324, 17155, 31553, 58038, 106743, 196331, 361106, 664183, 1221623, 2246918, 4132721, 7601259, 13980892, 25714875, 47297029, 86992802, 160004703, 294294531, 541292030, 995591267, 1831177831
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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+2*x+4*x^3+5*x^4+6*x^5)/(1-x-x^2-x^4-x^5-x^6).
a(3*n+3) = A001644(3*n+3) - 3*(-1)^n. (End)
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MAPLE
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A001643:=-(1+2*z+4*z**3+5*z**4+6*z**5)/(z+1)/(z**3+z**2+z-1)/(z**2-z+1); [Conjectured by Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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LinearRecurrence[{1, 1, 0, 1, 1, 1}, {1, 3, 4, 11, 21, 42}, 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+6*x^5)/(1-x-x^2-x^4-x^5-x^6)+x*O(x^n), n))
(Magma) I:=[1, 3, 4, 11, 21, 42]; [n le 6 select I[n] else Self(n-1) + Self(n-2) + Self(n-4) + Self(n-5) + Self(n-6): 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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