%I A020701
%S A020701 3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,
%T A020701 28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,
               3524578,
%U A020701 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 k-th order on the 
               space R^3. - Branko Malesevic (malesevic(AT)kiklop.etf.bg.ac.yu), 
               Feb 29 2004
%C A020701 Arxiv paper of 2007 generalizes Malesevic reference of 1998, giving recurrence 
               relations through dimension 10, for which case f(i+6) = 5f(i+4) - 
               6f(i+2) + f(i). - Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 
               07 2007
%D A020701 B. Malesevic: Some combinatorial aspects of differential operation composition 
               on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 
               9 (1998), 29-33.
%D A020701 B. Malesevic: Some combinatorial aspects of differential operation composition 
               on the space R^n, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. 
               9 (1998), 29-33.
%H A020701 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A020701 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A020701 B. Malesevic, <a href="http://matematika.etf.bg.ac.yu/publikacije/pub/
               P09(98)/P09_06.ZIP">Some combinatorial aspects of differential operation 
               composition on the space R^n </a>
%H A020701 Branko Malesevic, <a href="http://arXiv.org/math/pdf/0704.0750">Some 
               combinatorial aspects of differential operation compositions on space 
               R^n</a>, Apr 05 2007.
%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 (mathar(AT)strw.leidenuniv.nl), May 
               28 2008
%F A020701 G.f.: (3+2x)/(1-x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 19 2008]
%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)
%Y A020701 Subsequence of A000045, A020695. See A008776 for definitions of Pisot 
               sequences.
%Y A020701 Cf. A039834, A020695, A071679.
%Y A020701 Sequence in context: A080614 A079122 A071679 this_sequence A024885 A133605 
               A131354
%Y A020701 Adjacent sequences: A020698 A020699 A020700 this_sequence A020702 A020703 
               A020704
%K A020701 nonn
%O A020701 0,1
%A A020701 David W. Wilson (davidwwilson(AT)comcast.net)