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A020701
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Pisot sequences E(3,5), P(3,5).
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12
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3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
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
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REFERENCES
| 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.
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.
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LINKS
| Tanya Khovanova, Recursive Sequences
B. Malesevic, Some combinatorial aspects of differential operation composition on the space R^n
Branko Malesevic, Some combinatorial aspects of differential operation compositions on space R^n, Apr 05 2007.
Index to sequences with linear recurrences with constant coefficients, signature (1,1).
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FORMULA
| a(n) = Fib(n+4). a(n) = a(n-1) + a(n-2).
a(n)=A020695(n+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 28 2008
G.f.: (3+2x)/(1-x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2008]
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EXAMPLE
| 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)
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)
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MATHEMATICA
| CoefficientList[Series[(-2 z - 3)/(z^2 + z - 1), {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
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PROG
| (PARI) a(n)=fibonacci(n+4) \\ Charles R Greathouse IV, Jan 17 2012
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CROSSREFS
| Subsequence of A000045, A020695. See A008776 for definitions of Pisot sequences.
Cf. A039834, A020695, A071679.
Sequence in context: A080614 A079122 A071679 * A024885 A180459 A133605
Adjacent sequences: A020698 A020699 A020700 * A020702 A020703 A020704
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KEYWORD
| nonn,easy
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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