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 A187560 #36 Apr 11 2025 16:23:03
%S A187560 2,13,59,247,1007,4063,16319,65407,261887,1048063,4193279,16775167,
%T A187560 67104767,268427263,1073725439,4294934527,17179803647,68719345663,
%U A187560 274877644799,1099511103487,4398045462527,17592183947263,70368739983359,281474968322047,1125899890065407
%N A187560 a(n) = 4^(n+1)-2^n-1.
%C A187560 For n>0, binary numbers of the form (n+1)0 n, where n is the index value and the number of 1's. This can be formed by appending a leading 1 to the terms of A129868. It is also A156589 written in bit-reverse order.
%H A187560 Andrew Howroyd, <a href="/A187560/b187560.txt">Table of n, a(n) for n = 0..1000</a>
%H A187560 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F A187560 a(n) = 4^(n+1)-2^n-1 = A171499(n)-1.
%F A187560 G.f.: ( -2+x+4*x^2 ) / ( (x-1)*(2*x-1)*(4*x-1) ). - _R. J. Mathar_, Apr 09 2011
%F A187560 a(0)=2, a(1)=13, a(2)=59, a(n)=7*a(n-1)-14*a(n-2)+8*a(n-3). - _Harvey P. Dale_, Feb 25 2013
%F A187560 E.g.f.: exp(x)*(4*exp(3*x) - exp(x) - 1). - _Stefano Spezia_, Apr 11 2025
%e A187560 Binary values of the first 7 terms are 10, 1101, 111011, 11110111, 1111101111, 111111011111, 11111110111111.
%t A187560 Table[4^(n+1)-2^n-1,{n,0,30}] (* or *) LinearRecurrence[{7,-14,8},{2,13,59},30] (* _Harvey P. Dale_, Feb 25 2013 *)
%o A187560 (PARI) a(n)=4^(n+1)-2^n-1 \\ _Charles R Greathouse IV_, Nov 01 2015
%Y A187560 Cf. A171499.
%K A187560 nonn,easy
%O A187560 0,1
%A A187560 _Brad Clardy_, Mar 25 2011
%E A187560 Terms a(21) and beyond from _Andrew Howroyd_, Feb 25 2018