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 A048488 #40 Sep 08 2022 08:44:57
%S A048488 1,7,19,43,91,187,379,763,1531,3067,6139,12283,24571,49147,98299,
%T A048488 196603,393211,786427,1572859,3145723,6291451,12582907,25165819,
%U A048488 50331643,100663291,201326587,402653179,805306363,1610612731
%N A048488 a(n) = 6*2^n - 5.
%C A048488 a(n) = T(5, n), array T given by A048483.
%C A048488 Sequence is generated by the Northwest (NW) direction of circles put around circle(s). See illustration. - _Odimar Fabeny_, Aug 09 2008
%H A048488 Vincenzo Librandi, <a href="/A048488/b048488.txt">Table of n, a(n) for n = 0..1000</a>
%H A048488 Odimar Fabeny, <a href="/A082505/a082505.jpg">Illustration for this sequence</a>
%H A048488 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A048488 a(n) = 2*a(n-1) + 5, n > 0, a(0) = 1. - _Paul Barry_, Aug 25 2004
%F A048488 Equals binomial transform of [1, 6, 6, 6, ...]. - _Gary W. Adamson_, Apr 29 2008
%F A048488 a(n) = A000079(n)*6 - 5 = A007283(n)*2 - 5. - _Omar E. Pol_, Dec 21 2008
%F A048488 From _Colin Barker_, Sep 17 2012: (Start)
%F A048488 a(n) = 3*2^(1+n) - 5. a(n) = 3*a(n-1) - 2*a(n-2).
%F A048488 G.f.: (1+4*x)/((1-x)*(1-2*x)). (End)
%F A048488 a(n + 1) = 3 * 2^n - 5 = 1 + 2 * (Sum_{i=0..n-1} 3i) for n > 0. - _Gerasimov Sergey_ and _Alonso del Arte_, May 03 2014
%F A048488 a(n) = A000225(n+1)+4*A000225(n). - _R. J. Mathar_, Feb 27 2019
%e A048488 a(2) = 6 * 2^2 - 5 = 6 * 4 - 5 = 24 - 5 = 19.
%e A048488 a(3) = 6 * 2^3 - 5 = 6 * 8 - 5 = 48 - 5 = 43.
%p A048488 A048488:=n->6*2^n - 5; seq(A048488(n), n=0..30); # _Wesley Ivan Hurt_, May 09 2014
%t A048488 6(2^Range[0, 35]) - 5 (* _Alonso del Arte_, May 03 2014 *)
%o A048488 (Magma) [6*2^n - 5: n in [0..30]]; // _Vincenzo Librandi_, May 18 2011
%o A048488 (PARI) a(n)=6*2^n-5 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A048488 n-th difference of a(n), a(n-1), ..., a(0) is (6, 6, 6, ...).
%Y A048488 Cf. A000079, A007283. - _Omar E. Pol_, Dec 21 2008
%K A048488 nonn,easy
%O A048488 0,2
%A A048488 _Clark Kimberling_, Dec 11 1999
%E A048488 Simpler definition from _Ralf Stephan_