A140657 - OEIS

%I #38 Feb 27 2024 03:05:36

%S 4,-1,7,5,19,29,67,125,259,509,1027,2045,4099,8189,16387,32765,65539,

%T 131069,262147,524285,1048579,2097149,4194307,8388605,16777219,

%U 33554429,67108867,134217725,268435459,536870909,1073741827,2147483645,4294967299,8589934589

%N Powers of 2 with 3 alternatingly added and subtracted.

%H Jean-François Alcover and Vincenzo Librandi, <a href="/A140657/b140657.txt">Table of n, a(n) for n = 0..1000</a> (first 101 terms from Jean-François Alcover)

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

%F a(2n) = A000079(2n+1) + 3, a(2n+1) = A000079(2n+2) - 3.

%F a(n+1) - 2*a(n) = -9*A033999(n) = (-1)^(n+1)*A010734.

%F a(n) + a(n+1) = 3^*2^n = A007283(n).

%F a(2n) + a(2n+1) = A096045(n) + 2.

%F a(-n) = -A140683(n)/2^n.

%F O.g.f.: (4-5*x)/((1-2*x)(1+x)). - _R. J. Mathar_, Jul 29 2008

%F a(n) = 2^n+3*(-1)^n. - _R. J. Mathar_ , Jul 29 2008

%t LinearRecurrence[{1,2},{4,-1},40] (* or *) Total/@Partition[Riffle[ Table[ 2^n, {n,0,40}],{3,-3}],2] (* _Harvey P. Dale_, Nov 13 2014 *)

%t CoefficientList[Series[(4 - 5 x) / ((1 + x) (1 - 2 x)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jan 14 2015 *)

%o (Magma) [2^n+3*(-1)^n: n in [0..40]]; // _Vincenzo Librandi_, Aug 08 2011

%Y Cf. A000079, A007283, A010734, A033999, A096045, A140683.

%K sign,easy

%O 0,1

%A _Paul Curtz_, Jul 10 2008

%E Edited and extended by _R. J. Mathar_, Jul 29 2008

%E 4 inserted as first term and formulas accordingly updated by _Jean-François Alcover_, Jan 14 2015