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A007420
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Berstel sequence: a(n+1)=2a(n)-4a(n-1)+4a(n-2).
(Formerly M0030)
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4
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0, 0, 1, 2, 0, -4, 0, 16, 16, -32, -64, 64, 256, 0, -768, -512, 2048, 3072, -4096, -12288, 4096, 40960, 16384, -114688, -131072, 262144, 589824, -393216, -2097152, -262144, 6291456, 5242880, -15728640, -27262976, 29360128
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n) = 0 only for n = 0,1,4,6,13 and 52. [Cassels, following Mignotte. See also Beukers] - N. J. A. Sloane, Aug 29 2010
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REFERENCES
| F. Beukers, The zero-multiplicity of ternary recurrences, Composito Math. 77 (1991), 165-177.
J. W. S. Cassels, Local Fields, Cambridge, 1986, see p. 67.
G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; p. 28.
M. Mignotte, Suites recurrentes lineaires, Sem. Delange-Pisot-Poitou, 15-th year (1973/1974), No. 14, 9 pages.
Myerson, G. and van der Poorten, A. J., Some problems concerning recurrence sequences, Amer. Math. Monthly 102 (1995), no. 8, 698-705.
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 193.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..500
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FORMULA
| G.f.: x^2/(1-2*x+4*x^2-4*x^3).
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MAPLE
| A007420 := proc(n) options remember; if n <=1 then 0 elif n=2 then 1 else 2*A007420(n-1)-4*A007420(n-2)+4*A007420(n-3); fi; end;
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MATHEMATICA
| a[0]=a[1]=0; a[2]=1; a[n_]:=a[n]=2*a[n-1]-4*a[n-2]+4*a[n-3]; a/@ Range[0, 34] (* From Jean-François Alcover, Apr 06 2011 *)
LinearRecurrence[{2, -4, 4}, {0, 0, 1}, 40] (* From Harvey P. Dale, Oct 24 2011 *)
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PROG
| (Haskell)
a007420 n = a007420_list !! n
a007420_list = 0 : 0 : 1 : (map (* 2) $ zipWith (+) (drop 2 a007420_list)
(map (* 2) $ zipWith (-) a007420_list (tail a007420_list)))
-- Reinhard Zumkeller, Oct 21 2011
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CROSSREFS
| Cf. A035302.
A077953. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 07 2008]
Sequence in context: A111757 A022896 A100225 * A019219 A019139 A022904
Adjacent sequences: A007417 A007418 A007419 * A007421 A007422 A007423
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KEYWORD
| sign,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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