A101351 - OEIS

%I #25 Dec 07 2019 12:18:24

%S 2,4,9,18,36,71,140,276,545,1078,2136,4239,8424,16760,33377,66522,

%T 132668,264727,528468,1055340,2108097,4212014,8417264,16823583,

%U 33629456,67230256,134414145,268753266,537385140,1074573863,2148829916,4297145604,8593459169

%N a(n) = 2^n-1 + Fibonacci(n).

%H Colin Barker, <a href="/A101351/b101351.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-1,2).

%F a(n) = 4*a(n-1) -4*a(n-2) -a(n-3) +2*a(n-4). G.f.: x*(2-4*x+x^2)/((x-1) * (2*x-1) * (1-x-x^2)). - _R. J. Mathar_, Feb 06 2010

%F a(n) = ((1+sqrt(5))^n-(1-sqrt(5))^n)/(2^n*sqrt(5)) + 2^n - 1. - _Colin Barker_, Nov 02 2016

%p seq(2^x-1+fibonacci(x),x=1..30);

%t Table[2^n-1+Fibonacci[n],{n,30}] (* or *) LinearRecurrence[{4,-4,-1,2},{2,4,9,18},30] (* _Harvey P. Dale_, Aug 24 2012 *)

%o (Sage) [gaussian_binomial(n,1,2)+fibonacci (n) for n in range(1,31)] # _Zerinvary Lajos_, May 29 2009

%o (PARI) Vec(x*(2-4*x+x^2)/((1-x)*(1-2*x)*(1-x-x^2)) + O(x^30)) \\ _Colin Barker_, Nov 02 2016

%Y Cf. A000045, A033138.

%K nonn,easy

%O 1,1

%A _Jorge Coveiro_, Dec 25 2004

%E Offset changed to 1 by _Colin Barker_, Nov 02 2016