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A154879 Third differences of the Jacobsthal sequence A001045. 8

%I

%S 3,-2,4,0,8,8,24,40,88,168,344,680,1368,2728,5464,10920,21848,43688,

%T 87384,174760,349528,699048,1398104,2796200,5592408,11184808,22369624,

%U 44739240,89478488,178956968,357913944,715827880,1431655768,2863311528,5726623064

%N Third differences of the Jacobsthal sequence A001045.

%C Second differences of A078008. First differences of the sequence (-1)^(n+1)*A084247(n).

%H Vincenzo Librandi, <a href="/A154879/b154879.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).

%F a(n) + a(n+1) = A000079(n), n > 1.

%F a(n+3) = 8*A001045(n) = 4*A078008(n+1) = 2*A097073(n+1).

%F From _R. J. Mathar_, Jan 23 2009: (Start)

%F a(n) = a(n-1) + 2*a(n-2).

%F G.f.: (3-5*x)/((1+x)*(1-2*x)). (End)

%F a(n) = (1/3)*(8*(-1)^n + 2^n), with n >= 0. - _Paolo P. Lava_, Mar 02 2009

%t Differences[LinearRecurrence[{1,2},{0,1},40],3] (* or *) LinearRecurrence[ {1,2},{3,-2},40] (* _Harvey P. Dale_, Apr 20 2018 *)

%o (MAGMA) [(1/3)*(8*(-1)^n+2^n): n in [0..35]]; // _Vincenzo Librandi_, Jul 24 2011

%Y Cf. A115341.

%K sign,easy

%O 0,1

%A _Paul Curtz_, Jan 16 2009

%E Edited and extended by _R. J. Mathar_, Jan 23 2009

%E Typo in A-number in formula corrected by _R. J. Mathar_, Feb 23 2009

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Last modified April 18 06:48 EDT 2019. Contains 322209 sequences. (Running on oeis4.)