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 A241888 #63 Feb 20 2025 16:56:46
%S A241888 1,31,511,8191,131071,2097151,33554431,536870911,8589934591,
%T A241888 137438953471,2199023255551,35184372088831,562949953421311,
%U A241888 9007199254740991,144115188075855871,2305843009213693951,36893488147419103231,590295810358705651711,9444732965739290427391
%N A241888 a(n) = 2^(4*n + 1) - 1.
%H A241888 Jens Kruse Andersen, <a href="/A241888/b241888.txt">Table of n, a(n) for n = 0..100</a>
%H A241888 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).
%F A241888 a(n) = 2^(4*n + 1) - 1 = A000225(4*n + 1) = A013776(n) - 1 = 4*A000225(4*n - 1) + 3.
%F A241888 From _Colin Barker_, Aug 31 2014: (Start)
%F A241888 a(n) = 17*a(n-1) - 16*a(n-2).
%F A241888 G.f.: (14*x+1)/((x-1)*(16*x-1)). (End)
%F A241888 E.g.f.: exp(x)*(2*exp(15*x) - 1). - _Elmo R. Oliveira_, Feb 20 2025
%p A241888 seq(coeff(series((14*x+1)/((x-1)*(16*x-1)),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Mar 12 2019
%t A241888 Table[2^(4n + 1) - 1, {n, 0, 29}]
%t A241888 CoefficientList[ Series[(14x + 1)/((x - 1) (16x - 1)), {x, 0, 18}], x] (* _Robert G. Wilson v_, Jan 28 2015 *)
%t A241888 LinearRecurrence[{17,-16},{1,31},30] (* _Harvey P. Dale_, Mar 13 2016 *)
%o A241888 (PARI) vector(40, n, 2^(4*n-3)-1) \\ _Derek Orr_, Aug 11 2014
%o A241888 (PARI) Vec((14*x+1)/((x-1)*(16*x-1)) + O(x^100)) \\ _Colin Barker_, Aug 31 2014
%o A241888 (GAP) List([0..20],n->2^(4*n+1)-1); # _Muniru A Asiru_, Mar 12 2019
%Y A241888 Cf. A000225, A004171, A013776.
%K A241888 nonn,easy
%O A241888 0,2
%A A241888 _Wassan Letourneur_, Aug 09 2014