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A001643 A Fielder sequence.
(Formerly M2368 N0938)
2

%I M2368 N0938

%S 1,3,4,11,21,42,71,131,238,443,815,1502,2757,5071,9324,17155,31553,

%T 58038,106743,196331,361106,664183,1221623,2246918,4132721,7601259,

%U 13980892,25714875,47297029,86992802,160004703,294294531,541292030,995591267,1831177831

%N A Fielder sequence.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001643/b001643.txt">Table of n, a(n) for n = 1..1000</a>

%H Daniel C. Fielder, <a href="https://www.fq.math.ca/Scanned/6-3/fielder.pdf">Special integer sequences controlled by three parameters</a>, Fibonacci Quarterly 6, 1968, 64-70.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

%H Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 1, 1, 1).

%F 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).

%p 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.]

%t LinearRecurrence[{1, 1, 0, 1, 1, 1}, {1, 3, 4, 11, 21, 42}, 50] (* _T. D. Noe_, Aug 09 2012 *)

%o (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))

%o (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

%K nonn

%O 1,2

%A _N. J. A. Sloane_

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Last modified December 5 21:00 EST 2019. Contains 329779 sequences. (Running on oeis4.)