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A084247 a(n) = -a(n-1) + 2*a(n-2), a(0)=1, a(1)=2. 20

%I #34 Apr 24 2023 02:04:09

%S 1,2,0,4,-4,12,-20,44,-84,172,-340,684,-1364,2732,-5460,10924,-21844,

%T 43692,-87380,174764,-349524,699052,-1398100,2796204,-5592404,

%U 11184812,-22369620,44739244,-89478484,178956972,-357913940,715827884,-1431655764,2863311532

%N a(n) = -a(n-1) + 2*a(n-2), a(0)=1, a(1)=2.

%C Row sums of triangle in A112555. - _Philippe Deléham_, Sep 21 2009

%H Vincenzo Librandi, <a href="/A084247/b084247.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 Binomial transform of A084246.

%F a(n) = A077925(n-1) + 1.

%F a(n) = (4 - (-2)^n)/3.

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

%F E.g.f.: (4*exp(x) - exp(-2*x))/3.

%F a(n) = (-1)^(n+1)*(A078008(n+1) - A078008(n)). - _Paul Curtz_, Jun 30 2008, Feb 24 2021

%F a(n) = -2*a(n-1) + 4 . - _Philippe Deléham_, Sep 15 2009

%F a(n+1) = 2*A151575(n). - _Philippe Deléham_, Sep 21 2009

%F a(n) = A077925(n) + 3*A077925(n-1). - _R. J. Mathar_, Feb 24 2021

%t LinearRecurrence[{-1,2},{1,2},40] (* _Harvey P. Dale_, Nov 05 2016 *)

%o (Magma) [(4-(-2)^n)/3: n in [0..40]]; // _Vincenzo Librandi_, Aug 13 2011

%o (PARI) Vec((1+3*x)/((1-x)*(1+2*x)) + O(x^40)) \\ _Michel Marcus_, Feb 25 2016

%o (SageMath) [(4-(-2)^n)/3 for n in range(41)] # _G. C. Greubel_, Apr 24 2023

%Y Cf. A077925, A078008, A084246, A112555, A151575.

%K easy,sign

%O 0,2

%A _Paul Barry_, May 23 2003

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)