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A084247
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a(n) = -a(n-1) + 2a(n-2), a(0)=1, a(1)=2.
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18
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1, 2, 0, 4, -4, 12, -20, 44, -84, 172, -340, 684, -1364, 2732, -5460, 10924, -21844, 43692, -87380, 174764, -349524, 699052, -1398100, 2796204, -5592404, 11184812, -22369620, 44739244, -89478484, 178956972, -357913940, 715827884, -1431655764, 2863311532
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OFFSET
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0,2
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COMMENTS
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Second differences of Jacobsthal numbers, A001045. - Paul Curtz, Jun 30 2008
Binomial transform of A084246. a(n+1)=A077925(n)+1.
Row sums of triangle in A112555. [Philippe Deléham, Sep 21 2009]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-1,2).
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FORMULA
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a(n) = 4/3 - (-2)^n/3.
G.f.: (1+3x)/((1-x)(1+2x)).
E.g.f.: (4*exp(x)-exp(-2x))/3.
a(n) = -2*a(n-1)+4 . [Philippe Deléham, Sep 15 2009]
a(n+1) = 2*A151575(n). [Philippe Deléham, Sep 21 2009]
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MATHEMATICA
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LinearRecurrence[{-1, 2}, {1, 2}, 40] (* Harvey P. Dale, Nov 05 2016 *)
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PROG
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(MAGMA) [4/3-(-2)^n/3: n in [0..35]]; // Vincenzo Librandi, Aug 13 2011
(PARI) Vec((1+3*x)/((1-x)*(1+2*x)) + O(x^40)) \\ Michel Marcus, Feb 25 2016
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CROSSREFS
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Cf. A001045.
Sequence in context: A021493 A195395 A296805 * A300307 A286606 A266587
Adjacent sequences: A084244 A084245 A084246 * A084248 A084249 A084250
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry, May 23 2003
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STATUS
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approved
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