This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A020701 #65 Apr 08 2024 12:29:19
%S A020701 3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,
%T A020701 17711,28657,46368,75025,121393,196418,317811,514229,832040,1346269,
%U A020701 2178309,3524578,5702887,9227465,14930352,24157817,39088169,63245986,102334155,165580141
%N A020701 Pisot sequences E(3,5), P(3,5).
%C A020701 Number of meaningful differential operations of the (n+1)-th order on the space R^3. - _Branko Malesevic_, Feb 29 2004
%C A020701 Pisano period lengths: A001175. - _R. J. Mathar_, Aug 10 2012
%H A020701 Colin Barker, <a href="/A020701/b020701.txt">Table of n, a(n) for n = 0..1000</a>
%H A020701 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A020701 Branko Malesevic, <a href="https://www.jstor.org/stable/43666958">Some combinatorial aspects of differential operation composition on the space R^n</a>, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 9 (1998), 29-33.
%H A020701 Branko Malesevic, <a href="http://arxiv.org/abs/0704.0750">Some combinatorial aspects of differential operation compositions on space R^n</a>, arXiv:0704.0750 [math.DG], 2007.
%H A020701 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A020701 a(n) = Fib(n+4). a(n) = a(n-1) + a(n-2).
%F A020701 a(n) = A020695(n+1). - _R. J. Mathar_, May 28 2008
%F A020701 G.f.: (3+2*x)/(1-x-x^2). - _Philippe Deléham_, Nov 19 2008
%F A020701 a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-7+3*sqrt(5))+(1+sqrt(5))^n*(7+3*sqrt(5))))/sqrt(5). - _Colin Barker_, Jun 05 2016
%F A020701 E.g.f.: (7*sqrt(5)*sinh(sqrt(5)*x/2) + 15*cosh(sqrt(5)*x/2))*exp(x/2)/5. - _Ilya Gutkovskiy_, Jun 05 2016
%e A020701 Meaningful second-order differential operations appear in the form of five compositions as follows: 1. div grad f 2. curl curl F 3. grad div F 4. div curl F (=0) 5. curl grad f (=0)
%e A020701 Meaningful third-order differential operations appear in the form of eight compositions as follows: 1. grad div grad f 2. curl curl curl F 3. div grad div F 4. div curl curl F (=0) 5. div curl grad f (=0) 6. curl curl grad f (=0) 7. curl grad div F (=0) 8. grad div curl F (=0)
%t A020701 CoefficientList[Series[(-2 z - 3)/(z^2 + z - 1), {z, 0, 200}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jun 11 2011 *)
%t A020701 LinearRecurrence[{1,1},{3,5},40] (* _Harvey P. Dale_, Apr 22 2013 *)
%o A020701 (PARI) a(n)=fibonacci(n+4) \\ _Charles R Greathouse IV_, Jan 17 2012
%o A020701 (Magma) [Fibonacci(n-4): n in [8..80]]; // _Vincenzo Librandi_, Jul 12 2015
%Y A020701 Subsequence of A020695 and hence A000045. See A008776 for definitions of Pisot sequences.
%Y A020701 Cf. A039834, A020695, A071679, A116183.
%K A020701 nonn,easy
%O A020701 0,1
%A A020701 _David W. Wilson_