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Search: id:A007420
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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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+0
3
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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; listen)
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OFFSET
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0,4
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COMMENT
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a(n) = 0 only for n = 0,1,4,6,13 and 52. [Beukers] - Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 05 2000
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REFERENCES
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F. Beukers, The zero-multiplicity of ternary recurrences, Composito Math. 77 (1991), 165-177.
G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; p. 28.
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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FORMULA
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G.f.: x^2/(1-2*x+4*x^2-4*x^3).
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MAPLE
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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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CROSSREFS
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Cf. A035302.
A077953. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 07 2008]
Sequence in context: A111757 A022896 A100225 this_sequence A019219 A019139 A022904
Adjacent sequences: A007417 A007418 A007419 this_sequence A007421 A007422 A007423
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KEYWORD
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sign,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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