A166977 - OEIS

%I #12 Oct 31 2018 16:15:35

%S 0,1,5,7,17,31,65,127,257,511,1025,2047,4097,8191,16385,32767,65537,

%T 131071,262145,524287,1048577,2097151,4194305,8388607,16777217,

%U 33554431,67108865,134217727,268435457,536870911,1073741825,2147483647

%N Jacobsthal-Lucas numbers A014551, except a(0) = 0.

%C The sequence (-1)^n*a(n) is the inverse binomial transform of A166956.

%C The main diagonal of the table of a(n) and its higher differences in successive rows is 0,4,8,16,32,.. , 4*A131577(n).

%H G. C. Greubel, <a href="/A166977/b166977.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) = A014551(n), n>0.

%F a(n) - A001045(n) = A097073(n), n>0.

%F a(n) - A001045(n) = 4*A001045(n-1).

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

%F G.f.: x*(1 + 4*x)/((1+x) * (1-2*x)).

%F a(n) = (-1)^n + 2^n for n>0. - _Colin Barker_, Jun 06 2012

%F E.g.f.: exp(2*x) + exp(-x) - 2. - _G. C. Greubel_, May 30 2016

%t Join[{0, 1}, LinearRecurrence[{1, 2}, {5, 7}, 50]] (* or *) Table[2^n + (-1)^n, {n,1,25}] (* _G. C. Greubel_, May 30 2016 *)

%K nonn,less,easy

%O 0,3

%A _Paul Curtz_, Oct 26 2009

%E Edited and extended by _R. J. Mathar_, Mar 14 2010