A171501 - OEIS

%I #23 Sep 08 2022 08:45:50

%S 0,1,3,-1,7,-9,23,-41,87,-169,343,-681,1367,-2729,5463,-10921,21847,

%T -43689,87383,-174761,349527,-699049,1398103,-2796201,5592407,

%U -11184809,22369623,-44739241,89478487,-178956969,357913943,-715827881

%N Inverse binomial transform of A084640.

%C a(n) and differences are

%C 0,     1,   3,  -1,    7,   -9,

%C 1,     2,  -4,   8,  -16,   32,  =(-1)^(n+1) * A171449(n),

%C 1,    -6,  12, -24,   48,  -96,

%C -7,   18, -36,  72, -144,  288,

%C 25,  -54, 108, -216, 432, -864,

%C Vertical: 1) 0 followed with A168589(n).

%C           2) (-1 followed with A008776(n) ) signed. See A025192(n).

%C Main diagonal: see A167747(1+n). - _Paul Curtz_, Jun 16 2011

%H Vincenzo Librandi, <a href="/A171501/b171501.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) = A140966(n), n>0.

%F G.f.: x*(1+4*x) / ( (1+2*x)*(1-x) ). - _R. J. Mathar_, Jun 14 2011

%F a(1+n)= (-1)^(1+n) * A001045(1+n) + 2. - _Paul Curtz_, Jun 16 2011

%t CoefficientList[Series[x*(1 + 4*x)/((1 + 2*x)*(1 - x)), {x, 0, 30}], x]

%t LinearRecurrence[{-1,2},{0,1,3},40] (* _Harvey P. Dale_, Jan 14 2020 *)

%o (Magma) I:=[0, 1, 3]; [n le 3 select I[n] else -Self(n-1) + 2*Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Oct 18 2012

%K easy,sign

%O 0,3

%A _Paul Curtz_, Dec 10 2009

%E Mathematica program by _Olivier Gérard_, Jul 06 2011