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a(n) = (n+1) * 2^n - 1.
6

%I #28 Sep 08 2022 08:45:11

%S 0,3,11,31,79,191,447,1023,2303,5119,11263,24575,53247,114687,245759,

%T 524287,1114111,2359295,4980735,10485759,22020095,46137343,96468991,

%U 201326591,419430399,872415231,1811939327,3758096383,7784628223,16106127359,33285996543,68719476735

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

%C Row sums of triangle in A018900 (without the initial 0). - _Reinhard Zumkeller_, Jun 24 2009

%H Vincenzo Librandi, <a href="/A087323/b087323.txt">Table of n, a(n) for n = 0..3000</a> (corrected by Ray Chandler, Jan 19 2019)

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).

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

%F a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). G.f.: x*(3-4*x)/((1-x)*(1-2*x)^2). - _Colin Barker_, Mar 23 2012

%F a(n) = A001787(n+1) - 1. - _Omar E. Pol_, Nov 09 2013

%t Table[(n + 1)2^n - 1, {n, 0, 29}] (* _Alonso del Arte_, Jan 31 2014 *)

%t LinearRecurrence[{5,-8,4},{0,3,11},40] (* _Harvey P. Dale_, Sep 15 2019 *)

%o (Magma) [((n+1)*2^n - 1): n in [1..30]]; // _Vincenzo Librandi_, Sep 29 2011

%Y Cf. A087322 (a triangle which includes this sequence as the leading diagonal but without the initial zero).

%K nonn,easy

%O 0,2

%A _Amarnath Murthy_, Sep 03 2003

%E Edited and extended by _David Wasserman_, May 06 2005

%E Formula promoted to definition and offset adjusted to 0 by _Alonso del Arte_, Jan 31 2014