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 A001649 A Fielder sequence. (Formerly M2649 N1056) 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES 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). LINKS 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 and Conjectures, Université du Québec à Montréal, 1992. Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 0, 1). FORMULA 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). MAPLE 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.] MATHEMATICA 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 *) PROG (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 CROSSREFS Sequence in context: A131076 A001648 A051054 * A303220 A301894 A213215 Adjacent sequences:  A001646 A001647 A001648 * A001650 A001651 A001652 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 25 12:29 EDT 2019. Contains 322455 sequences. (Running on oeis4.)