|
%I #27 Dec 28 2022 13:35:58
%S 1,5,15,39,95,223,511,1151,2559,5631,12287,26623,57343,122879,262143,
%T 557055,1179647,2490367,5242879,11010047,23068671,48234495,100663295,
%U 209715199,436207615,905969663,1879048191,3892314111,8053063679
%N a(n) = (n+1)*2^(n-1) - 1.
%C Row sums of triangle A135852. - _Gary W. Adamson_, Dec 01 2007
%C Binomial transform of [1, 4, 6, 8, 10, 12, 14, 16, ...]. Equals A128064 * A000225, (A000225 starting 1, 3, 7, 15, ...). - _Gary W. Adamson_, Dec 28 2007
%H G. C. Greubel, <a href="/A099035/b099035.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).
%F a(n) = A057711(n+1) - 1 = A058966(n+3)/2 = (A087323(n)-1)/2 = (A074494(n+1)-2)/3 = (A003261(n+1)-3)/4 = A036289(n+1)/4 - 1, n>0.
%F a(n) = A131056(n+1) - 2. - _Juri-Stepan Gerasimov_, Oct 02 2011
%F From _Colin Barker_, Mar 23 2012: (Start)
%F a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3).
%F G.f.: x*(1-2*x^2)/((1-x)*(1-2*x)^2). (End)
%F E.g.f.: ((2*x+1)*exp(2*x) - 2*exp(x) + 1)/2. - _G. C. Greubel_, Dec 31 2017
%t Table[(n + 1)*2^(n - 1) - 1, {n,1,30}] (* _G. C. Greubel_, Dec 31 2017 *)
%t LinearRecurrence[{5,-8,4},{1,5,15},30] (* _Harvey P. Dale_, Dec 28 2022 *)
%o (PARI) a(n)=(n+1)*2^(n-1)-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Magma) [(n+1)*2^(n-1) -1: n in [1..30]]; // _G. C. Greubel_, Dec 31 2017
%Y First differences of A066524.
%Y Cf. A135852, A128064, A000225.
%K nonn,easy
%O 1,2
%A _Ralf Stephan_, Sep 28 2004
|
