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A001640
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A Fielder sequence.
(Formerly M3358 N1352)
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2
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1, 1, 4, 9, 16, 28, 43, 73, 130, 226, 386, 660, 1132, 1947, 3349, 5753, 9878, 16966, 29147, 50074, 86020, 147764, 253829, 436036, 749041, 1286728, 2210377, 3797047, 6522681, 11204863, 19248056, 33064889, 56799857, 97572504, 167612993, 287930658, 494615964
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OFFSET
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1,3
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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+3*x^2+4*x^3+5*x^4+6*x^5)/(1-x-x^3-x^4-x^5-x^6).
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MAPLE
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A001640:=-(1+3*z**2+4*z**3+5*z**4+6*z**5)/(-1+z+z**3+z**4+z**5+z**6); # conjectured by Simon Plouffe in his 1992 dissertation
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MATHEMATICA
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LinearRecurrence[{1, 0, 1, 1, 1, 1}, {1, 1, 4, 9, 16, 28}, 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+3*x^2+4*x^3+5*x^4+6*x^5)/(1-x-x^3-x^4-x^5-x^6)+x*O(x^n), n))
(Magma) I:=[1, 1, 4, 9, 16, 28]; [n le 6 select I[n] else Self(n-1) + Self(n-3) + 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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