This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A171389 #37 Feb 06 2025 10:38:27
%S A171389 20,41,83,167,335,671,1343,2687,5375,10751,21503,43007,86015,172031,
%T A171389 344063,688127,1376255,2752511,5505023,11010047,22020095,44040191,
%U A171389 88080383,176160767,352321535,704643071,1409286143,2818572287
%N A171389 a(n) = 21*2^n - 1.
%H A171389 Vincenzo Librandi, <a href="/A171389/b171389.txt">Table of n, a(n) for n = 0..1000</a>
%H A171389 Gennady Eremin, <a href="https://arxiv.org/abs/2405.16143">Partitioning the set of natural numbers into Mersenne trees and into arithmetic progressions; Natural Matrix and Linnik's constant</a>, arXiv:2405.16143 [math.CO], 2024. See pp. 3, 14.
%H A171389 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A171389 a(n+1) = 2*a(n) + 1.
%F A171389 G.f.: (20-19*x)/((1-x)*(1-2*x)). - _Vincenzo Librandi_, Jul 06 2012
%F A171389 a(n) = 3*a(n-1) - 2*a(n-2). - _Vincenzo Librandi_, Jul 06 2012
%F A171389 a(n) + a(n-1)^2 = (a(n-1) + 1)^2. - _Vincenzo Librandi_, Jun 11 2014
%p A171389 A171389:=n->21*2^n-1; seq(A171389(n), n=0..40); # _Wesley Ivan Hurt_, Jun 11 2014
%t A171389 CoefficientList[Series[(20-19*x)/((1-x)*(1-2*x)),{x,0,40}],x] (* _Vincenzo Librandi_, Jul 06 2012 *)
%o A171389 (BASIC) for j = 0 to 30 : print str$((21*2^j)-1)+", "; : next j [_Jeremy Gardiner_, Oct 23 2011]
%o A171389 (Magma) I:=[20, 41]; [n le 2 select I[n] else 3*Self(n-1)-2*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jul 06 2012
%Y A171389 Cf. A086224, A175805.
%K A171389 nonn,easy
%O A171389 0,1
%A A171389 _Vincenzo Librandi_, Dec 07 2009
%E A171389 Edited by _Jon E. Schoenfield_, Jun 23 2010
%E A171389 Offset changed to 0 and first formula corrected by _Jeremy Gardiner_, Oct 23 2011