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 A122041 #21 Sep 08 2022 08:45:27 %S A122041 23,45,89,177,353,705,1409,2817,5633,11265,22529,45057,90113,180225, %T A122041 360449,720897,1441793,2883585,5767169,11534337,23068673,46137345, %U A122041 92274689,184549377,369098753,738197505,1476395009,2952790017 %N A122041 a(n) = 2*a(n-1) - 1 for n>1, a(1)=23. %C A122041 From a quiz. %H A122041 G. C. Greubel, <a href="/A122041/b122041.txt">Table of n, a(n) for n = 1..1000</a> %H A122041 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2). %F A122041 a(n) = A083683(n). - _R. J. Mathar_, Aug 02 2008 %F A122041 a(n) = 11*2^n + 1 for n>=1. - _Paolo P. Lava_, Oct 01 2008 %F A122041 a(n) = 3*a(n-1) - 2*a(n-2), a(1)=23, a(2)=45. - _Harvey P. Dale_, Dec 13 2012 %F A122041 From _G. C. Greubel_, Oct 04 2019: (Start) %F A122041 G.f.: x*(23 - 24*x)/((1-x)*(1-2*x)). %F A122041 E.g.f.: 11*exp(2*x) + exp(x) - 12. (End) %e A122041 23x2 -1 = 45; 45x2 -1 = 89; 89x2 -1 = 177; 2x177 -1 = 353. %p A122041 seq(1 + 11*2^n, n=1..30); # _G. C. Greubel_, Oct 04 2019 %t A122041 NestList[2#-1&,23,30] (* or *) LinearRecurrence[{3,-2},{23,45},30] (* _Harvey P. Dale_, Dec 13 2012 *) %o A122041 (PARI) a(n)=if(n>1,2*a(n-1)-1,23); for(n=1,40,print1(a(n),",")) %o A122041 (Magma) [1+11*2^n: n in [1..30]]; // _G. C. Greubel_, Oct 04 2019 %o A122041 (Sage) [1+11*2^n for n in (1..30)] # _G. C. Greubel_, Oct 04 2019 %o A122041 (GAP) List([1..30], n-> 1 + 11*2^n); # _G. C. Greubel_, Oct 04 2019 %K A122041 nonn %O A122041 1,1 %A A122041 Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 14 2006