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%I M2367 N0937 #38 Sep 08 2022 08:44:29
%S 1,3,4,11,21,36,64,115,211,383,694,1256,2276,4126,7479,13555,24566,
%T 44523,80694,146251,265066,480406,870689,1578040,2860046,5183558,
%U 9394699,17026986,30859771,55930361,101368389,183720435,332975581,603486148,1093760479
%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="/A001642/b001642.txt">Table of n, a(n) for n = 1..1000</a>
%H Daniel C. Fielder, <a href="http://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="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 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_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 1, 1).
%F G.f.: x(1+2x+4x^3+5x^4)/(1-x-x^2-x^4-x^5).
%p A001642:=-(z+1)*(5*z**3-z**2+z+1)/(-1+z+z**2+z**4+z**5); # conjectured by _Simon Plouffe_ in his 1992 dissertation
%t LinearRecurrence[{1, 1, 0, 1, 1}, {1, 3, 4, 11, 21}, 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)/(1-x-x^2-x^4-x^5)+x*O(x^n),n))
%o (Magma) I:=[1,3,4,11,21]; [n le 5 select I[n] else Self(n-1) + Self(n-2) + Self(n-4) + Self(n-5): n in [1..30]]; // _G. C. Greubel_, Jan 09 2018
%K nonn
%O 1,2
%A _N. J. A. Sloane_
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