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A084247 a(n) = -a(n-1) + 2a(n-2), a(0)=1, a(1)=2. 17
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,2).

FORMULA

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]

MATHEMATICA

LinearRecurrence[{-1, 2}, {1, 2}, 40] (* Harvey P. Dale, Nov 05 2016 *)

PROG

(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

CROSSREFS

Cf. A001045.

Sequence in context: A147980 A021493 A195395 * A286606 A266587 A070692

Adjacent sequences:  A084244 A084245 A084246 * A084248 A084249 A084250

KEYWORD

easy,sign

AUTHOR

Paul Barry, May 23 2003

STATUS

approved

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Last modified June 27 15:01 EDT 2017. Contains 288790 sequences.