%I #30 Sep 08 2022 08:45:49

%S 2,4,7,14,27,54,107,214,427,854,1707,3414,6827,13654,27307,54614,

%T 109227,218454,436907,873814,1747627,3495254,6990507,13981014,

%U 27962027,55924054,111848107,223696214,447392427,894784854,1789569707

%N a(n) = (10*2^n + 3 - (-1)^n)/6.

%H Vincenzo Librandi, <a href="/A171231/b171231.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).

%F a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3), n >= 3.

%F a(n+1) - a(n) = A048573(n-1).

%F a(n) = 2*A000975(n+1) - 3*A000975(n-1).

%F a(n) - a(n-2) = 5*2^n.

%F a(n+1) - 2*a(n) = ((-1)^n-1)/2 = -A000035(n).

%F G.f.: ( 2-3*x^2 ) / ( (x-1)*(2*x-1)*(1+x) ). - _R. J. Mathar_, Jul 07 2011

%F a(n) = ceiling( (5/3)*(2^n) ). - _Wesley Ivan Hurt_, Jun 28 2013

%t LinearRecurrence[{2,1,-2},{2,4,7},40] (* _Harvey P. Dale_, Feb 11 2015 *)

%o (PARI) a(n)=(10<<n+3)\/6 \\ _Charles R Greathouse IV_, Jul 07 2011

%o (Magma) [( 10*2^n+3-(-1)^n )/6: n in [0..40]]; // _Vincenzo Librandi_, Aug 05 2011

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Dec 05 2009

%E Definition replaced by the Lava formula of 2009. Contents converted to formulas. - _R. J. Mathar_, Jul 07 2011