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%I M3358 N1352 #37 Sep 08 2022 08:44:29
%S 1,1,4,9,16,28,43,73,130,226,386,660,1132,1947,3349,5753,9878,16966,
%T 29147,50074,86020,147764,253829,436036,749041,1286728,2210377,
%U 3797047,6522681,11204863,19248056,33064889,56799857,97572504,167612993,287930658,494615964
%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="/A001640/b001640.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 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, 1, 1, 1).
%F G.f.: x*(1+3*x^2+4*x^3+5*x^4+6*x^5)/(1-x-x^3-x^4-x^5-x^6).
%p A001640:=-(1+3*z**2+4*z**3+5*z**4+6*z**5)/(-1+z+z**3+z**4+z**5+z**6); # conjectured by _Simon Plouffe_ in his 1992 dissertation
%t LinearRecurrence[{1, 0, 1, 1, 1, 1}, {1, 1, 4, 9, 16, 28}, 50] (* _T. D. Noe_, Aug 09 2012 *)
%o (PARI) a(n)=if(n<0,0,polcoeff(x*(1+3*x^2+4*x^3+5*x^4+6*x^5)/(1-x-x^3-x^4-x^5-x^6)+x*O(x^n),n))
%o (Magma) I:=[1,1,4,9,16,28]; [n le 6 select I[n] else Self(n-1) + Self(n-3) + Self(n-4) + Self(n-5) + Self(n-6): n in [1..30]]; // _G. C. Greubel_, Jan 09 2018
%K nonn
%O 1,3
%A _N. J. A. Sloane_
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