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A001649
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A Fielder sequence.
(Formerly M2649 N1056)
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1
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1, 3, 7, 15, 26, 57, 106, 207, 403, 788, 1530, 2985, 5812, 11322, 22052, 42959, 83675, 162993, 317491, 618440, 1204651, 2346534, 4570791, 8903409, 17342876, 33782050, 65803777, 128178646, 249678140, 486346022, 947349461, 1845334319, 3594511719, 7001720167
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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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T. D. Noe, Table of n, a(n) for n = 1..1000
Daniel C. Fielder, Special integer sequences controlled by three parameters, Fibonacci Quarterly 6, 1968, 64-70.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 0, 1).
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FORMULA
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G.f.: x*(1+2*x+3*x^2+4*x^3+6*x^5)/(1-x-x^2-x^3-x^4-x^6).
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MAPLE
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A001649:=-(1+2*z+3*z**2+4*z**3+6*z**5)/(z+1)/(z**5-z**4+2*z**3-z**2+2*z-1); # [Conjectured by Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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LinearRecurrence[{1, 1, 1, 1, 0, 1}, {1, 3, 7, 15, 26, 57}, 50] (* T. D. Noe, Aug 09 2012 *)
CoefficientList[Series[x*(1+2*x+3*x^2+4*x^3+6*x^5)/(1-x-x^2-x^3-x^4-x^6), {x, 0, 50}], x] (* G. C. Greubel, Dec 19 2017 *)
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PROG
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(PARI) a(n)=if(n<0, 0, polcoeff(x*(1+2*x+3*x^2+4*x^3+6*x^5)/(1-x-x^2-x^3-x^4-x^6)+x*O(x^n), n))
(MAGMA) I:=[1, 3, 7, 15, 26, 57]; [n le 6 select I[n] else Self(n-1) + Self(n-2) + Self(n-3) + Self(n-4) + Self(n-6): n in [1..30]]; // G. C. Greubel, Dec 19 2017
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CROSSREFS
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Sequence in context: A131076 A001648 A051054 * A303220 A301894 A213215
Adjacent sequences: A001646 A001647 A001648 * A001650 A001651 A001652
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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