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 A001643 A Fielder sequence. (Formerly M2368 N0938) 2
 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 (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, Appendix to Thesis, Montreal, 1992 Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1. Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 1, 1, 1). FORMULA 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). MAPLE 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.] MATHEMATICA LinearRecurrence[{1, 1, 0, 1, 1, 1}, {1, 3, 4, 11, 21, 42}, 50] (* T. D. Noe, Aug 09 2012 *) PROG (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 CROSSREFS Sequence in context: A110865 A152982 A001642 * A247171 A005218 A219514 Adjacent sequences:  A001640 A001641 A001642 * A001644 A001645 A001646 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 16 07:59 EDT 2021. Contains 343030 sequences. (Running on oeis4.)