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 A103459 #24 Sep 08 2022 08:45:16 %S A103459 1,9,65,513,4097,32769,262145,2097153,16777217,134217729,1073741825, %T A103459 8589934593,68719476737,549755813889,4398046511105,35184372088833, %U A103459 281474976710657,2251799813685249,18014398509481985,144115188075855873 %N A103459 a(n) = 8^n + 1 - 0^n. %C A103459 a(n)^3 is palindromic in base 8 (1_8, 1331_8, 1030301_8, 1003003001_8, ...). %H A103459 G. C. Greubel, <a href="/A103459/b103459.txt">Table of n, a(n) for n = 0..1000</a> %H A103459 Patrick De Geest, <a href="http://www.worldofnumbers.com/index.html">World!Of Numbers</a> %H A103459 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8). %F A103459 G.f.: (1-8*x^2)/((1-x)*(1-8*x)). %F A103459 a(n) = Sum_{k=0..n} binomial(n, k)*0^(k(n-k))*8^k. %F A103459 a(n) = A062395(n), n > 0. - _R. J. Mathar_, Aug 28 2008 %F A103459 a(n) = 8*a(n-1) - 7, with a(1)=9. - _Vincenzo Librandi_, Dec 29 2010 %F A103459 a(n) = 9*a(n-1) - 8*a(n-2); a(0)=1, a(1)=9, a(2)=65. - _Harvey P. Dale_, Oct 21 2011 %F A103459 E.g.f.: -1 + exp(x) + exp(8*x). - _G. C. Greubel_, Jun 23 2021 %t A103459 Join[{1},8^Range[20]+1] (* or *) Join[{1},LinearRecurrence[{9,-8},{9,65},20]] (* _Harvey P. Dale_, Oct 21 2011 *) %o A103459 (Magma) [1] cat [8^n + 1: n in [1..30]]; // _G. C. Greubel_, Jun 23 2021 %o A103459 (Sage) [1]+[8^n+1 for n in (1..30)] # _G. C. Greubel_, Jun 23 2021 %Y A103459 Cf. A046233, A062395. %K A103459 easy,nonn %O A103459 0,2 %A A103459 _Paul Barry_, Feb 07 2005